So, you've got a protagonist who's a bit abrasive, a bit rough around the edges. If you wanted to make a love interest for that character (assuming the character is the type that has the human capacity for love), you could either make the love interest just like the protagonist, make them single, or Take a Third Option: you could make their love interest completely passive.
The inversion of All Girls Want Bad Boys and All Amazons Want Hercules, Pitbull Dates Puppy is when someone who's tough and Not Good with People enters a relationship with The Woobie, Non-Action Guy, The Heart, or the Extreme Doormat — often by force, though it is possible for one or the other to naturally fall in love with each other.
Often done in historical romance novels where a badass decides to marry some fresh young innocent thing as a change from his usual Vamp or Femme Fatale choices. May be a Romantic False Lead if done deliberately to screw with a more suitable ex.
Contrast Best Her to Bed Her. Also see True Love Is Exceptional for when a similar Opposites Attract dynamic actually works out, and Aggressive Submissive when the relationship works like this most of the time, until the time they actually have sex, when suddenly their roles get inverted. Compare Beast and Beauty, Masculine Girl, Feminine Boy, and Brooding Boy, Gentle Girl.
In psychology, this is known as the "precarious couple."
- Lua and Ladd from Baccano! may have fit this trope, with Lua, by the end, almost getting up the courage to suggest that maybe she doesn't want to die by his hand.
- The bloodthirsty Cute and Psycho Miyamiya from Bamboo Blade has the unassuming Gonk boy Dan for a boyfriend. She never really demonstrates the especially violent aspects of her personality around him, however. It's occasionally hinted that Dan has his own dark side. He's just less easily provoked and hides it better even when he is.
- Black Lagoon has the kind, caring Non-Action Guy Rock and the homicidal, bloodthirsty criminal Revy.
- Gajeel and Levy from Fairy Tail. Gajeel is a rough and violent Blood Knight literally Made of Iron and Levy is a short, sweet and friendly Cute Bookworm.
- Fruits Basket has Kyo as the pitbull (ironic due to his zodiac year) to Tohru's puppy. In the early chapters, Kyo was verbally aggressive to her and even accidentally hits her at one point, but he gets better and learns to control his temper around her.
- Future Diary has the psychotic, violent and possessive Yandere Yuno who is completely obsessed with the cowardly Extreme Doormat Yukiteru. Taken to an extreme when she kidnaps him, ties him to a chair and keeps him drugged for an entire week, to ensure that he'd stay "safe".
- Kara no Kyoukai has a variation of this with Nice Guy Kokuto and Sociopathic Hero Shiki. In one case taken to its logical extreme when Shiki once puts a knife to his throat and threatens to kill him. Eventually, it works out when she lets him be her Morality Pet.
- Chessmaster megalomaniac Char Aznable of Mobile Suit Gundam first dated Lahla Sune, a sweet, demure Hindu girl (though she's also a Tyke Bomb), and then later dated the similarly-dispositioned Nanai Miguel. Taken to the extreme in the novels, where he ultimately winds up with a plump Girl Next Door named Margaret who works as a secretary (which may have been the whole point, as the sort of people he usually meets through his work aren't really the kind anyone sane would want to start a family with).
- In Monthly Girls' Nozaki-kun, careless troublemaker Seo is curiously fond of her good-natured underclassman Wakamatsu. Played With in that Waka wants to make Seo feel bad so she won't bother him anymore, but fails in ways that make him look like he's invested in their relationship.
- Neon Genesis Evangelion: At heart, Shinji and Asuka truly care about and are attracted to each other, but Shinji's extreme passivity and Asuka's similarly over-the-top aggressiveness prevent them from forming a real relationship during the series.
- Kanou and Ayase from Okane Ga Nai, accentuated even more by their massive height difference. Their relationship is supposed to work out somehow but they've got a long way to go, considering that Kanou's still extremely forceful and dominant over the frail, would-rather-martyr-himself-than-harm-even-his-would-be-rapists Ayase 7 volumes in.
- In Onidere, gang leader Saya is head over heels for nerdy Tadashi.
- Flipped around all over the place with Toradora!. Ryuuji has the Face of a Thug, so much so that on the way to class one morning, two guys gave him their wallets, pleading for their lives. He's actually a very nice guy, as well as a major Neat Freak. Contrast with Taiga, who's a short, very cute girl... and known around school as the "Palmtop Tiger" for her angry demeanor and occasional violent outbursts (she punches out Ryuuji when he accidentally bumps into her).
- Yandere Kanojo:
- The delinquent-girl Reina and unassuming stoic guy Manabu fall for one another. Hilarity Ensues as Reina tries (vainly) to keep their relationship a secret in order to preserve her reputation.
- Generation Xerox for Reina's parents, Cute and Psycho Ran and Shrinking Violet Kouichiro.
- The Principal who is a Stern Teacher and Heroic Comedic Sociopath has a Fragile Flower of a wife
- In Crystar Crystal Warrior, the short, tough-as-nails warrior woman Shen is the much older, somewhat bumbling wizard Ogeode's wife. She's completely devoted to him and won't tolerate anyone insulting him in her presence; he meanwhile seems a little intimidated by her. They have a daughter, the beautiful sorceress Ika.
- The Joker and Harley Quinn's relationship. True, Harley is psychotic and destructive like Joker, but is still much more innocent. Their relationship is usually Joker abusing Harley, though it's occasionally implied that he does actually care about her.
- In Killer Condom, bear Bob "Bladder" and Plumley, a normal sized mature man who manages to look quite like a puppy next to the incredibly hairy mountain of meat, Bob.
- For Neon Genesis Evangelion fics, there are these:
- In Advice and Trust, Shinji's female schoolmates don't understand why he is infatuated with Asuka because they think that she's a brutish tsundere and he a timid wallflower.
- The Child of Love: Asuka could be very abrasive and overbearing, especially at the early stages of her pregnancy when she was madder and more depressed, and Shinji was pretty meek and wimpy, but both were drawn to each other.
- Evangelion 303: Asuka is a very aggressive, hot-headed woman and Shinji is a non-confrontational, quiet, shy man. Asuka always claimed she wanted to someone confident, determined and muscular and she was not interested in scrawny boys. Still she fell in love with Shinji and after seducing him they are unable to live without each other.
- In Ghosts of Evangelion, Asuka is bold, aggressive, and she can get nasty and mean when she's in a bad mood. Shinji is more passive and acquiescent. If someone asks him why they are together, he answers that he owes her, he doesn't really mind her bad moods, she is real nice when she wants (and she doesn't mean most bad things she says), and she actually wants him to be assertive and stand up for himself.
- HERZ: Kurumi often wondered why Shinji -a quiet, unassuming guy- married a fiery woman as Asuka. In reality Shinji and Asuka need each other desperately and they think no one else will ever be able to understand their pain.
- Last Child of Krypton: Despite of her abrasive, bold nature, Asuka could not help to be drawn to quiet, non-belligerent, unasuming, polite Shinji. And it was Shinji's kind nature that allowed him seeing she was a better, kinder person than she thought she was despite her aggressive, forward behaviour, and falling in love with her. Subverted when she discovered he was Superman.
- Superwomen of Eva 2: Lone Heir of Krypton: Asuka is fiery, hot-blooded, aggressive, hard-headed, impatient... and she is Supergirl. Shinji is a Non-Action Guy passive, quiet and meek. However, Shinji fell in love with Asuka precisely because he admired her strength, willpower, courage and determination, and Asuka fell in love with him precisely because he was gentle, caring and dependable.
- Subverted in Thousand Shinji. At first sight, Asuka seems to be the pitbull to Shinji's puppy because she is brash, loud and demanding, whereas Shinji is quieter... But in reality Shinji is the pitbull. A conniving, crafty, manipulative pitbull.
- Children of an Elder God: Although they're less damaged than their canon counterparts, Asuka is still pretty aggressive and combative, and her Love Interest Shinji is pretty wimpy and timid, so their relationship looks like this to their friends.
- The Second Try subverted it. Everyone thinks Shinji and Asuka's relationship is this because Shinji is wimpy and meek and Asuka is harsh and aggressive. In reality their relationship got over that phase several years ago, but they pretend otherwise in order to keep their time-travelling status secret.
- Neon Genesis Evangelion: Genocide: Shinji and Asuka's relationship is pretty difficult and complex since Asuka is very abrasive and bitter due to a dismal childhood and deep trauma, and Shinji is somewhat wimpy. Nonetheless, it gets better when Shinji makes a serious effort to support and help Asuka, and she mellows down when she acknowledges that he cares about her. Shinji also comes to find that trying to appeal to Asuka's better nature in an argument often works much better than being confrontational with her.
- Once More with Feeling: Since Asuka is abrasive, loud and temperamental and Shinji is quiet, calm and non-confrontational, most of their acquaintances consider that they have this kind of relationship. Touji and Kensuke think their "poor" friend Shinji needs to be saved from the "Demon Red", and Misato doesn't get how Shinji appears to be utterly, impossibly immune to everything Asuka throws at him in her standard attempts to push him away.
- WALL•E has its title character and EVE. WALL•E is The Woobie and a very sweet, caring robot who only wants someone to love after spending hundreds of years alone, while his love interest EVE is a tough Action Girl prone to blowing things up with her plasma cannon at the slightest provocation.
- In Wreck-It Ralph, the short, sweet, and Nice Guy Fix-It Felix Jr. gets paired up with grizzled Action Girl Space Marine Tamora Calhoun.
- A Brother's Price: In the backstory, we have quiet-spoken, dignified Alannon, who was married to a band of rough soldiers in an Exotic Extended Marriage. In the present, there is Cullen Moorland, a sweet, innocent and thoroughly harmless boy, who gets married to Alannon's granddaughters, the Whistler sisters, who are anything but harmless.
- Jaded English spy James of Your Scandalous Ways resolves to marry some sweet innocent girl when he gets back home, as he's really sick of Femme Fatales. (This doesn't happen.)
- Kethry of the Heralds of Valdemar series—a tough mercenary sorceress whose lack of combat training is made up for by a magic sword—ends up Happily Married to Jadrek, a brilliant and learned Non-Action Guy who suffers from severe arthritis (incapacitating when they meet, later somewhat alleviated by magic).
- The Hunger Games: Katniss and Peeta. While neither of them is a trained warrior, Katniss was taught archery by her father, and regularly hunts for the family. Peeta is the baker's son from her village. His skills are cake-decoration and talking to people. There is a love-triangle with Katniss childhood friend Gale. Which is resolved when Katniss decides to be with Peeta, who is a better match because he's so gentle and nice, just what cynical Katniss needs.
- The human lead of The General series, Raj Whitehall, is a gifted officer from a frontier province that generally provides soldiers rather than taxes to the Civil Government. However in the pit of backstabbing, manipulation, murder, and other entertainments that is the political scene of East Residence; the man is a puppy. His petite, beautiful wife Suzette? She is the pitbull, made all more vicious for wanting to keep the man she loves intact.
- Matthias of A World Less Visible is a an alpha werewolf with some minor anger management issues. His boyfriend, Daniel, is a skinny twink and Empathic Healer who tends to throw up around violence.
- Mix Beer With Liquor And You Will Get Sicker has protagonist Lauchlan as the Puppy; he's extremely shy, polite, kind-hearted, and lacks social skills as well as assertiveness. Corbin, the man he falls in love with, is a blunt, rude, ever-cussing, cynical Pitbull who's not intimidated by anyone.
- Herr Flick and Helga on 'Allo 'Allo!. Played for Laughs in that the roles tend to switch between the two - Helga is usually entirely submissive to Flick and even fears him a little, but she is also the more experienced in sexual matters which tend to frighten him.
- Ally McBeal: John Cage, nicknamed "Biscuit", is a sensitive dorky lawyer who dates a gorgeous but icy Nelle Porter (nicknamed "Sub-zero") in season 2 and 3. Their relationship is quite happy and Nelle gets a bit warmer, but they later break up.
- Quinn, who began as the Alpha Bitch of the series, and Finn, the Big Man on Campus who just happens to be a really Nice Guy. During the time they were together, they genuinely were in love with each other, but Quinn slept with Finn's best friend and tried to pass the baby off as Finn's and Finn himself kissed Rachel while he and Quinn were still together.
- Alpha Bitch Quinn follows this up when she starts dating dorky but cute nerd Sam Evans.
- Santana and Brittany. Santana can be a bitch and Brittany is an adorable Cloud Cuckoolander, Brittany's the only person Santana is genuinely nice to and the only one that can actually control Santana's meanness.
- House has two doctors who date in season 4 and tried to keep their relationship secret. The pitbull is Amber whose nickname is "Cutthroat Bitch" and the puppy is Wilson, a rather sweet sensitive guy. Part of the arc of their relationship was her trying to teach him to stand up for himself, even to her. Their relationship lasted for half a season. She died in season finale.
- In a medical drama Monday Mornings, Dr. Sydney Napur dates Dr. John Lieberman. He asks her out in the first episode but she kind of made him by almost-screaming and being pushy. Generally, she is way tougher than him. When Sydney discusses it with her colleagues, Bald, Black Leader Guy Dr. Jorge Villanueva thinks he'll "go through her like crap through goose", and she gets angry. Dr. Lieberman reacts with a Flat "What.".
- April and Andy on Parks and Recreation. They get married, and it seems to work, probably because April is actually a softie under the snarky exterior. His main tactic to get her back when she was trying to make him jealous and toying around with him? Being nice and inviting her revenge boyfriend to jam with him on old Dave Matthews Band songs.
- Darlene and David's relationship on Roseanne. Darlene is a somewhat aggressive snarker, and David's terrible homelife has left him completely downtrodden.
- Veronica Mars
- Bad boy Logan (pitbull) and The Ingenue Hanna (puppy).
- Princely Young Man Duncan (puppy) and Jerk with a Heart of Gold Veronica (pitbull). She and Piz had a similar dynamic.
- Rich Bitch Jackie (pitbull) and Dogged Nice Guy Wallace (puppy) had shades of this too.
- By the end of the series debatably, Logan (puppy) and Veronica (pitbull)
- Rather common in BioWare RPGs, usually with a protagonist on the darker end of the Morality Meter:
- Aggressive!Hawke with Cloud Cuckoo Lander Merrill in Dragon Age II. Interestingly enough, this can still occur down the Friendship path as easily as the Rivalry path.
- The Warden in Dragon Age: Origins can be played as a rather grim, vindictive, and aggressive character, and still get together with Alistair the perfect gentleman or Leliana the sweet former nun.
- The Warden can be an Incorruptible Pure Pureness — innocent and selfless all-around Nice Guy and get with the quasi-Token Evil Teammates, the Social Darwinist snarkywitch Morrigan or the blithe Professional Killer cassanovian Zevran.
- In Left 4 Dead, Francis, a hot-blooded biker who enjoys fighting and stealing stuff, falls for cute little news reporter Rochelle. She reciprocates. Everyone else is thoroughly confused.
- Metal Gear:
- Metal Gear Solid: There's clearly something going on between Sniper Wolf and Otacon. While Otacon's massive crush for her is not entirely requited, she still is very fond of him. But even though she puts on a tough appearance, she's actually a Death Seeker and knows it will be only more painful for him if they get closer.
- Meryl and Johnny in Metal Gear Solid 4. He is a complete loser and dork, while she's one of the toughest Action Girls in video game land, and has a rather mean temper as well. She shows no interest in him at all and constantly berates him for most of the game, until he saves her life not once but twice, after which she admits her affection for him, but is still quite mean most of the time. When he finally asks her to marry him, she refuses on the ground that in this relationship SHE has to propose to him, which he then gladly accepts.
- Yuri and Alice in Shadow Hearts. He's a rude, crude brawler with a bunch of demons fused to his soul, and she's a sweet, gentle White Magician Girl exorcist. It takes them a very long time to admit it, but they're pretty head-over-heels for each other.
- Implied with Rita and Estelle in Tales of Vesperia, though it gets no further than subtext. Rita's aggressive and pragmatic, whilst Estelle is noble, naive and sweet. She's also the only one who brings out Rita's softer side.
- Parodied in Hark! A Vagrant's "Strong Female Characters" story, where Susan B. Assthony becomes enticed by the "incredibly weak male lead" character, and apparently marries him.
- Deconstructed with Vriska and Tavros. Vriska's a Manipulative Bitch who crippled Tavros for a laugh as a child, and years later, continues to mess with him to try and toughen him up. It later turns out that part of the reason she's doing it is to try and invoke Generation Xerox. Her ancestor wound up in love with (and was killed by) Tavros' ancestor, who incidentally was one of the greatest heroes trollkind had ever known. In the end, Vriska finally winds up killing him because she feels he's toughened up too late. Vriska and Tavros finally start dating in the afterlife, and their relationship is every bit as messed up and dysfunctional as you'd expect. It doesn't last long, of course.
- Vriska's relationship with John reconstructs the trope, mostly because she's learned from her past experiences "helping" people. Not only does she succeed with him in every way she failed with Tavros, but she actually starts wanting to be a better person as a result. Unfortunately, she's killed right after she asks him out on a date.
- In Bad Machinery Mildred and Jack have a mutual interest in each other, but he's an extremely nervous good boy while she recently stole a car. At the end of "The Case of the Severed Alliance" he turns her down because of this.
Jack: Mildred I like you but... I think you might be...
[turns and runs away]
Jack: A dangerous nutter!!
The Rant: Mildred and Jack: star-crossed lovers or a fox and a chicken? I'm really not sure. I don't think they're sure either.
- Janet Barch and Timothy O'Neill on Daria. A man-hating divorcee and borderline Straw Feminist falls for and dates (and eventually marries) a shy, neurotic, utterly inoffensive Hippie Teacher after O'Neill gives her an impromptu therapy session about venting her feelings over being divorced.
- KaBlam!'s Henry and June. June is a hot-tempered, deadpan, tough, bossy girl with a crush on Henry, who isn't that strong or smart.
- Clingy Jealous Girl Eska and Bolin in The Legend of Korra, for the brief period they were together. Eska treats Bolin like her slave, and when he essentially leaves her at the altar she gets very pissed. (Keep also in mind that while Bolin may have been a naïve little creampuff at that point in the story, he is an earthbender and a badass in his own right; it's simply that Eska was just that scary.)