Most critics of the series (and even a small portion of Twilight fans) see Edward and Bella's relationship as twisted, controlling and abusive due to things like Edward breaking into Bella's home, watching her sleep, stealing her belongings, breaking her truck so she can't see other people, putting her under house arrest, threatening, talking down to and manipulating her. Not to mention when he leaves her in New Moon–he (seemingly) wipes all traces of himself in her house, including photographs she took of him, and–with zero emotion or pain whatsoever–tells Bella he doesn't love her anymore. Did we mention this makes her fall into catatonia?
Also the relationship between Jacob and Renesmee, Bella's weird half-human-half-vampire child. Jacob imprints on her before she's even conceived, and they both to fall in love with each other, when she is still a baby. Also, Renesmee will never look older than 18. Unfortunate Implications makes it feel like pedophilia to quite a few readers.
It's based in the concept of the soul mate, where in a woman is destined to be with her husband even before she physically exists and after her death. The concept itself may be morally and philosophically flawed in a lot of peoples eyes, but that doesn't change the fact that it is the internal logic by which the story operates. It's the same logic used to explain why Edward and Bella are meant to be together despite not having known each other very long and not seeming to have much of an interpersonal bond or anything in common. Not to mention the fact that he was born a good century before she was.
Word of God states that hybrids are born with an adult intelligence and sense of morality. Considering Renesmee does things like bite Jacob when she doesn't get what she wants fast enough, learns very quickly how to manipulate him, and the fact that the imprint literally makes it impossible for him to do anything she doesn't like, a strong argument can be made that, while their relationship is indeed abusive, Renesmee is the abuser.
In fact, this interpretation could be pushed even further with adding that Bella could be seen as a mashup of The Vamp, the Black Widow, the Manipulative Bitch, the Bitch in Sheep's Clothing and the Baroness who tries to act all sweet and vulnerable, but whose primary motivation is herself and what she wants, and certainly not love. And what does she want? Gaining power and eternal life by manipulating Edward into believing she truly loves him, so as to have him nail her and bite her. And keeping Jacob as a plan B in case the Edward option fails. She's basically the character that teaches young girls how to manipulate and control men. Except she's not, because both these relationships hinge on the two boys thinking they are in love with her, one because of the vampire mate issue and the other because of some unresolved wolf imprint issue. If girls really wanted to learn how to manipulate men, they should probably start with the original Vampire Diaries or The Wheel of Time books or something.
Bella has Borderline Personality Disorder, which means very variable moods, black and white thinking, idealization (like when she describes vampires and especially Edward), unstable interpersonal relationships (Team Edward or Team Jacob), unstable self-image (she describes herself plain but it doesn't seem like it), no identity of her own, very insecure (that's actually what causes the "plot"), she's suicidal etc.
Bella has Histrionic Personality Disorder, a condition characterized by unstable emotions and distorted self image. She has most of the symptoms associated with the condition, particularly the desire to be the center of attention. Among other symptoms, she is self-centered, overly concerned with physical appearance, making rash decisions and not thinking before acting, attempting suicide for attention... Really, if you look through a list of symptoms, she easily fits nearly all of them.
Bella has Schizotypal Personality Disorder, which means she comes across as cold or aloof (more to the audience than to the characters, admittedly); behaves in an odd, eccentric or peculiar manner; tends towards voluntary social isolation and a poor rapport with others; a tendency towards / fascination with "magical" ideas or thinking (in this case, vampirism); suspicious or paranoid ideas (her running inner commentary on other women and their "shallow" attraction towards Edward, or her arrogant beliefs about non-vampires in general); vague and often stereotypical thinking and beliefs; and obsessive ruminations (compulsive preoccupation with the symptoms of ones distress) often of an aggressive or sexual content (in this case, desperately wanting to sleep with Edward and thinking that this will solve all problems between them); depersonalization; de-realization. She especially fits the Insipid Schizotypal subtype, which includes, schizoid, depressive and dependant features, since she is clearly overly-dependant when it comes to Edward and spends much of the time alone or depressed.
Bella has Narcissistic Personality Disorder. Expects to be recognized as superior and special, without superior accomplishments? Chapter 26 of Breaking Dawn ended with what was pretty much an extended whine-fest about how Bella never got the praise she deserved until she was a vampire. Expects constant attention, admiration and positive reinforcement from others? Bella whined about Edward ignoring her when they first met even though she claimed not to like him at that point. She acted like her friends were in the wrong when they gave up on her after she went crazy for four months because Edward left her, and the ones that didn't come crawling back when she was ready for their attentions again were outright called evil with no irony. When Jacob stopped spending time with Bella because he turned into a werewolf she outright stalked him. Pretty much anyone that doesn't kiss Bella's feet is treated as being a horrible person and always in the wrong. Envies others and believes others envy her? She's horribly envious of all vampires, the Cullens in particular, and was convinced that envy was at the root of her female classmates' dislike of her. Is preoccupied with thoughts and fantasies of great success, enormous attractiveness, power, intelligence? The moment she thinks that vampirism is the key to all of these things, she becomes obsessed with becoming one. Lacks the ability to empathize with the feelings or desires of others? There's not enough space on this page to list every example. Probably the most glaring was when she couldn't understand her father being upset that she vanished for three days while he was at his best friends funeral. Is arrogant in attitudes and behavior? Even before she became a vampire, Bella was horribly arrogant and her internal monologue went on and on and on about how non-vampires aren't good enough for her. It got even worse after she was turned. Has expectations of special treatment that are unrealistic? See under the expects constant attention and positive reinforcement note. That's seven out of seven.
Some might interpret most of the series as Bella being in a coma from the stress of trying to choose between two seemingly conflicting interests. Edward represents her want to preserve the memory of the dead and Jacob represents her want to make the future a better place. The reason we get hardly any description of her is because she has lost sight of her own self. Forks is chosen as the setting to serve the "a fork in the road" symbolism.
Cleolinda has stated several times that things make a lot more sense if you think of it like Bella being Too Kinky to Torture and actually being turned on by the stalking and control, instead of it being played as True Love for Her Own Good.
Some have jokingly suggested that the reason why Vampires can't read Bella's mind is because she literally has no character to speak of.
"No no, you can read it, it's just that there is nothing there!"
– Rifftrax, when Edward tells Bella he can read everyone's mind but hers.
Is James a hedonistic monster who wants to eat all humans, or is he a guy with poor impulse control who's labeled evil for remembering a plot point that the Cullens didn't?
Jacob - Sweet, well-intentioned best friend in love wronged by the manipulative heroine who is too dumb to notice that he is the better choice and acts reckless a couple of times as a result? Or immature, selfish jerk who shows his True Colors as soon as he knows he can't get into Bella's pants?
Carlisle - A kindly doctor who hates what he is and genuinely strives to protect humanity and do good in the world? Or a sadistic man who enjoys playing God, turning people into vampires because he wants companions and doing very little to actually keep humans safe from the vampires he creates?
Alice - A perky Manic Pixie Dream Girl who simply has an overzealous love for fashion and dressing people up? Or an empty woman who sees others as dolls for her to play with and who only does things because her visions tell her to and not because she actually understands them?
In some ways, she appears to be an even worse sociopath than Bella. Bella regularly shows contempt for other people's feelings and opinions. Alice doesn't seem to understand that other people can even have feelings and opinions. Witness Bella's birthday in the second book and wedding in the fourth book. Bella wants to keep it low key. Alice casually disregards this and makes grand sweeping plans on her own, neither asking Bella's permission beforehand nor seeking her forgiveness afterwards. She even threatens to force Bella to attend the birthday party if Bella won't come and be a good birthday girl of her own volition.
Esme - A sweet Team Mom who has built up a happy life after nothing but tragedy? Or a Stepford Smiler who plays mommy to a number of unrelated adults to avoid the pain of an eternity of postpartum depression?
In this review of Twilight, the reviewer says that the Vampire-Werewolf Love Triangle of Bella, Edward and Jacob could be interpreted as a racial-class thing, since vampires in the book (and in general) tend to be sort of wealthy European types and werewolves are butch blue collar Native Americans.
This Reddit post posits the idea that the series is a tragedy, rather than a romance.
Edward- A tortured, romantic, Byronic Hero who is willing to do anything for his beloved but is genuinely afraid that he may hurt her? Or a sadistic ego-maniac who intentionally encourages Bella's unhealthy emotional dependence on him, manipulates her into socially isolating herself to such an extent that there is nothing important in her life except him, deliberately leads her into danger that only he can protect her from and then proceeds to emotionally and psychologically torture her by repeatedly threatening to abandon her and requiring her to give up more and more of her own identity in order to remain with him just because he gets off on knowing that he has complete control over another person.
The third option is that he's a flawed but sympathetic character who wants to do right by Bella but has a horrible grasp of acceptable behaviour towards a love interest, which might be forgivable in the context of his forced social isolation over the last 90 years were it not for the fact that Bella rarely calls him out on the worst of it.
The Volturi can be seen as being more heroic than the designated protagonists, the Cullens, at times. Although they don't particularly value human lives, they are the only vampires that attempt to keep some sort of order. They stopped the Southern wars and the senseless slaughter of both vampires and humans, and they outlawed the horrifying existence of the immortal children and punished those who created one in the first place. The so called 'good' vampires that supposedly value human life, the Cullens, did nothing about the slaughter of humans in Seattle when they were perfectly capable of stopping the slaughter, think the Volturi were too extreme in outlawing the immortal children and killing those that created, and condone and assist the group of vampires they gathered as witnesses in hunting humans.
According to this post (scroll down to the end) from DasSporking's founder Mervin, vampiric transformation warps the personality of the changed. In short:
Carlisle: was a devout who believed in the good of people; now a Tautological Templar who believes that he's doing God's will, so he and his family can't do wrong.
Edward: was a Spoiled Brat; now he does and takes anything he wants, and he can't comprehend why anyone would deny him, a vampire, anything.
Esme: an abused wife; now a Flat Character who's defined solely by her role as "mother".
Rosalie: was a vain person, though that was due to her upbringing and was harmless. Now she wants to be the most beautiful and (possibly) a mother, and she's ready to kill to do it.
Emmet: was the classic "have-some-fun-with-brawls" boy; now he sees everything as a fun brawl.
Alice: she wanted to be accepted, but she was locked in an asylum due to her visions; now she is a flashy snob who will do anything to make sure her predictions come true.
Jasper: was a soldier in the civil war; now he's a Blood Knight who will manipulate others without a second thought.
Bella: she was a shallow teenager prone to Wangst and Wants To Be Special; now she is the bestest thing around, though she'll panic when an actual threat arrives.
Leah Clearwater; Vindictive harpy who just needs to move on and be happy for her ex, or Only Sane Man who's horribly abused for not tolerating everyone else's insanity and jerkassery.
The whole story is meant to be experimental. Said experiments are as follows. What if...
Had a hero who in most other stories would probably be the villain.