In American Dragon: Jake Long, Jake's mythology teacher and minor antagonist Hans Rotwood insists on being called "Professor", not "Mister".
Animaniacs: Whenever someone mentions the Warner brothers, expect Dot to pipe up with "And the Warner sister!"
Another variation shows up in "Broadcast Nuisance".
Slam Fondlesome: I will not have my broadcast interrupted by a bunch of little kids! Yakko: We protest you calling us "little kids"! We prefer to be called "vertically-impaired pre-adults".
The Archer episode "Skytanic" has the repeated insistence that the titular ship isn't a zeppelin, but a rigid airship filled with helium. Archer never gets it, constantly referring to the thing as a hydrogen-filled death trap.
Lana: ...and what part of that are you still not getting? Archer: Well, obviously the whole concept, Lana! We didn't all go to science camp!
EVERYONE refers to Trinette's son as "the wee baby Seamus." Every. Single. Time.
Also done with regards to Trinette herself in the episode "Training Day", who is a call girl. When Cyril thinks he accidentally killed her, Archer calls her a hooker because "...when they're dead, they're just hookers."
Ray's brother Randy isn't a drug dealer, he's a drug farmer
The Legend of Korra: Varrick allegedly committed the crimes of arson, kidnapping, terrorism, and grand larceny. ALLEGEDLY.
Varrick: Never convicted! Asami: That's because you escaped before the trial. Varrick: I didn't escape, The Universe decided to set me free!
The Boondocks features recurring character "A Pimp Named Slickback", who gets flustered whenever people refer to him simply as Slickback and constantly has to correct them. A Pimp Named Slickback actually makes this correction a part of his introduction in one episode: "Please say the entire thing. Yes, that includes the 'A Pimp Named' part. Yes, every time."
In Cranberry Christmas, Mr. Whiskers and Cyrus Grape get into an argument over who owns a nearby body of water, and whether or not it is a pond or a cranberry bog. Any time it is mentioned throughout the special, the other will insist that his term is the correct one. Cyrus even does this to the audience. "That's right; I said pond."
In the episode "Once Upon a Dime" had Scrooge McDuck wearing a kilt and correcting some non-Scots who called it a skirt.
Also, Scrooge never makes a "colossal blunder" when making decisions. A "business failure" maybe, but never a colossal blunder. (He's never made a "business failure" either, and never intends to start, but should he ever truly lose money on an poorly done and/or ill-conceived investment or project, that's the term he prefers.)
On Family Guy, Peter learns he has a black ancestor who was a slave and tries to embrace his roots, adopting the name "Kichwa Tembo", which he insists on being called, until his father-in-law offers him reparations.
Carter: Not enough? Fine. Make it $20,000. How do you spell Kichwa? Peter: Yeah, you know what? Screw the Kichwa. Make it out to Peter. P-E-T-E...
In an episode of The Flintstones, Fred is employed as an apartment complex's janitor. "Not janitor! Resident stationary engineer!"
In Grandpa Pig's Train To The Rescue, Gertrude is not a little train, she is a miniature locomotive. In order, this is insisted by Grandpa Pig, Peppa, all the other passengers, then finally Mrs Rabbit (whose big train had broken down.)
In The Golden Boots, Peppa insists that her boots are "golden," but Suzy feels that they're simply "yellow." They get into an Argument of Contradictions about it.
In the Wizard of Oz parody episode of Phineas and Ferb, Doctor Doofenshmirtz (playing the Wicked Witch of the West) is insistent that he's a warlock, not a witch. The credits even list him as "Doofenwitch," with "witch" crossed out and replaced with "warlock".
From the episode "Candace Gets Busted": It's not a party, it's an intimate get-together!
Buford wasn't crying. He was sweating through his eyes. Major Monogram later said the same thing in the movie. (see above)
Again with Buford when he allowed Doofenshmirtz and his date to enter Phineas and Ferb's platypus-themed restaurant without a reservation. Doof didn't bribe Buford. He, to quote Buford, "caught my attention in a monetary fashion".
A downplayed example but Phineas and Ferb are each other's brothers rather than stepbrothers, Candace is Ferb's sister rather than stepsister, Linda is Ferb's mom rather than stepmom and Lawrence is Phineas and Candace's dad rather than stepdad (in fact, it's hard for first time viewers to tell that the Flynn-Fletchers are a blended family at all).
In an episode of Rocky and Bullwinkle, a Southern Gentleman insists that people call The American Civil War "The War Between The States". This sort of bickering over historical and political terminology is very much Truth in Television. Actually he gets peeved over any word or phrase that even sounds like "Civil". When the next episode was going to be titled "Civil Defense", he angrily blustered, "War — I say — War between the States Defense!" (Amazingly enough, he's supporting the good guys, who are cast as the Confederate Army, though not by choice.) He relents after the war is reenacted (on the football field) and the South wins.
Girl: Milhouse has cooties! Milhouse: It's called lice, and it's nothing to be ashamed of!
Homer meeting the President of the Globex Corporation:
Homer: Wow, my boss.
Hank Scorpio: Don't call me that word. I don't like things that elevate me above the other people. I'm just like you. Oh, sure, I come later in the day, I get paid a lot more, and I take longer vacations, but I don't like the word "boss".
In one episode, Lisa points out that she's a perfectly reasonable child in order to stand up for children's rights at the town hall. An onlooker immediately reacts in shock, saying that he'd thought she was a midget. "First of all, they prefer to be called 'little people,' and secondly..."
In a parody of Artificial Intelligence, there was a robot urinal that doesn't like being called an urinal-bot. He prefers to be called "Lava-tron".
The man Marge bought a ticket from wasn't a scalper. He was a "dude whose 200 friends did not show up".
The Springfield Nuclear Power Plant melts down once, but meltdown is "one of those annoying buzzwords. We prefer to call it an unrequested fission surplus." Homer saves the plant/town through sheer dumb luck.
Homer does not want to take a vacation in Florida ("America's wang"). "They prefer the Sunshine State," though.note Very much Truth in Television, as this is the state's official nickname. For every sunny day, though, there's a pretty high hurricane risk.
When Lisa and Bart unleash a zombie plague on Springfield, he chides her for calling them zombies: "They prefer to be called the living impaired."
This exchange from "Treehouse of Horror VII" section The Thing and I:
Dr. Hibbert: You don't forget a thing like... Siamese twins! Lisa: I believe they prefer to be called "conjoined twins". Dr. Hibbert: And hillbillies prefer to be called "sons of the soil", but it ain't gonna happen.
Lampooned in the "Treehouse of Horror VIII" section The Homega Man:
Moe: Actually, Homer, we resent being called 'mutants'. We prefer 'freaks'. Or 'monsters'.
The writers insist that Waylon Smithers is not gay, he is a "Burns-sexual".
In Storm Hawks' first episode, the team is registering at the Sky Knight council. The registrar asks if Radaar is a pet, and when Radaar gets mad, Aerrow steps in to explain that Radaar prefers to be called the "mission specialist".
In one episode of Total Drama All-Stars, Chris keeps calling the Playa (now his private home), a cottage. Every time he does it, Courtney protests that it's actually a mansion. In a later episode, Zoey also calls him out for it.
In the animated Trolls de Troy series, Waha is a human girl adopted by trolls, a race of quite hairy humanoids. As such, she's very touchy about being called hairless or mangy, instead insisting that she has a "thwarted pilosity".
Dr. Orpheus from The Venture Bros. is a necromancer. Although he'll be the first to admit that he uses that title because Sorcerer or Magician sounds goofy nowadays.
W.I.T.C.H.: Blunk is no smuggler, he's a retailer.
Wonder Pets: The Wonder Pets had a tendency to refer to any baby animal as a "baby x," i.e. a "baby cow." A baby cow is called a "calf." This occasionally led to ridiculousness, such as a "baby kitten" or worse, a "baby egg."
Yogi's Gang: Yogi takes it for an insult if his hobo friend Smiley is called a "bum". Justified because, as Smiley explains it, a hobo looks for work and that makes them different from bums.