If you're familiar with the Twilight universe, you know that Bella and Edward have an unhealthy relationship. A LiveJournal user has detailed fifteen ways, using a list from the National Domestic Violence hotline. Is that why Twilight's so "romantic"?
In Edward and Bella's relationship, he's controlling, he threatens to commit suicide, he throws her through a glass table, he's jealous of her outside relationships and sometimes loses his temper and damages property when angry. Romantic! But what about stories like Romeo & Juliet? Or Beauty And The Beast? Suicide, violence and death are often at the core of great love stories.
While it makes for glorious, romantic subject matter, all-consuming, obsessive love is, in itself, "unhealthy." Telling someone that you can't live without her sounds romantic, but any therapist would probably diagnose that kind of talk as dysfunctional and codependent. Yet love stories are full of characters — Heathcliff in Wuthering Heights; Satine in Moulin Rouge; the couple in Pretty Woman — who are often liars, cads or ne'er do wells with psychological issues (fear of commitment, etc).
The thing about teenage love, especially, is that it feels like life or death even when vampires are not involved. The characters in flicks like Sixteen Candles, 10 Things I Hate About You and Say Anything take love so seriously that they could also be deemed "unhealthy," with the right diagnosis. In New Moon, Bella is thrown into truly dangerous situations — where her life is actually in peril — and it only functions to make the movie more romantic. He saves her, he represses the urge to bite her, he'd go to Italy and stand in the sun and kill himself if she ever died. Falling for someone — and being vulnerable — is already dangerous, in a way; love stories often just ramp up the drama with peril. While it's not cool that Edward is controlling of Bella, it seems like we, as a culture, love questionable romantic heroes and rebels without causes. Would we even know it was love if there was no danger? Edward and Bella may be in an emotionally abusive relationship, but she's not the first — and we, as an audience, seem to like it that way.