They hate Twilight for the same reasons misogynists actually do.

On her official website, Meyer responds to feminist allegations that Bella is weak and easily led. “There are those who think my stories are misogynistic – damsel in distress must be rescued by strong hero.” But to Meyer that isn’t who Bella is. She points out that, in New Moon, the second book in the series, Bella must contend with Edward leaving. Meyer reminds her fans and her detractors alike that Bella is not mourning an ordinary teen romance but rather the loss of the love of her life, her other half, her soul mate. And perhaps this is the reason for the series’ massive success among modern young women. In his August 2008 Washington Post article, Twilight Sinks Its Teeth Into Feminism, Leonard Sax posits, “Three decades of adults pretending that gender doesn’t matter haven’t created a generation of feminists who don’t need men; they have instead created a hoard of girls who adore the traditional male and female roles and relationships in the Twilight saga.”

And there are those who actually just thought we were pissed because we were "feminist women." I can't imagine what they'd say to this.

Well, what about wikipedia's page on Domestic abuse, especially under emotional abuse?

Same thing!

Oh, but then, you think I'm just looking for something to bitch about, don't you? I want to hate on a romance and I have no idea what fiction is. Because that's another thing, isn't it. It's just fiction! It can't do any real harm! It's not real! Just fun! It can't cause any problems because it's just a book, right?! It won't have a bad or damaging influence. Because it's fiction, we're just being stupid and bitchy, right?
Ok, so yeah. Bella and Edward are imaginary. But that doesn't make it okay or safe.It DOES have an influence on girls my age. And the thing is, it has nothing to do really with Bella. She really doesn't matter despite being the narrator. No it's all Edward.

Yes, I've heard my girlfriends, ones I know to be fully against sexism and such, actually say to each other, "Well, I think Edward is the most perfect boyfriend you can have. I want to have a boyfriend just like him."

Oh, but they don't mean abuse!

Examples of Edward’s Creepy Control Issues
-He tries to control who Bella is friends with (with the handy excuse that her friend is a werewolf, enemy of the vampires).
-He refuses to turn Bella into a vampire despite her wishes, For Her Own Good.
-He refuses to have sex with Bella since he “won’t be able to control himself” if they do. Buffy, of course, turned this icky rape-culture stereotype on its head. There is no such consciousness here.
-He won’t allow Bella to make her own decisions regarding . . . ok, basically anything. Edward calls the shots, period.

So yeah, he doesn’t beat her. Other than that, they are the very picture of after-school-special abusive relationship. (Full disclosure – I was so disgusted with New Moon I never bothered to read Eclipse, the third in the series. If anything improved in #3, please let me know!)

This is the legacy of our kick-ass vampire slayer feminist icons? –sigh-

The following one is great, since she sees no contradiction between these two sections:

In my own opinion (key word), the foundation of feminism is this: being able to choose. The core of anti-feminism is, conversely, telling a woman she can't do something solely because she's a woman—taking any choice away from her specifically because of her gender. "You can't be an astronaut, because you're a woman. You can't be president because you're a woman. You can't run a company because you're a woman." All of those oppressive "can't"s.

One of the weird things about modern feminism is that some feminists seem to be putting their own limits on women's choices. That feels backward to me. It's as if you can't choose a family on your own terms and still be considered a strong woman. How is that empowering? Are there rules about if, when, and how we love or marry and if, when, and how we have kids? Are there jobs we can and can't have in order to be a "real" feminist? To me, those limitations seem anti-feminist in basic principle."

[No warning of the change of tack, here. It's like it's written by two different people. However, it is on the same page. Listed as written by the same woman.]

Really, Meyer? What about the allegations of abuse by Bella's love interest, Edward? Like the way he dismantles her car so she can't see her friends? Locks her in his house for the same reason? Or how Bella jumps of a cliff (literally) just to "hear his voice in her head"?

Bella's choices are troubling, sure, but it's the blatant romanticism of what she and her interest does, excuses of him doing these things "out of love" and "to protect her" that makes her an anti-feminist figure and indeed make you one as well.

For a contrasting opinion from whiskey:

Edward Cullen wins the girl in Twilight by being the most dominant and controlling male in Bella's life. Superman wins Lois Lane by being ... mostly Clark Kent, the mild mannered reporter. Lois herself is independent, and while lacking powers has opinions and a mind to match her beauty. This is the male heroic model that worked, that built Western Civilization, and males resent it's overthrow by the female-tween fantasies of Twilight and other vampire-fantasy fads. Lois is desirable because she's winnable, and winnable by more than just superpowers and wealth and power, otherwise Lex Luthor would have married her. Her very independence and intelligence make her winnable, by Clark Kent not Superman, and it means she stays won. Clark does not have to constantly mate-guard her like Cullen does Bella.

For girls, Twilight teaches them to be passive, eschew education and a career, forget a traditional family with a traditional husband who while not "sexy and dangerous" is faithful and loving, and sacrifice warm, loving, and emotionally intimate relations based on the mind as well as raw sexual desire, for pure adrenaline based excitement. Twilight explicitly teaches girls to abandon their minds and intellect for their emotions and lusts. In short, a how-to for girls to enter into inevitably abusive and emotionally destructive bad-boy relationships, in the desire to "change" and control a powerful, dangerous man.