----------
The haters of twilight as I hear it (I never read it cause I'm not a teen in love) is it breaks all the known mythology of Vampires and Werewolves. That is a hard thing to get past. Vampires do not sparkle in sunlight they burn to death
----------
That's why some people hate it, sure, but plenty of books, shows and games break the basic conventions of what constitutes a vampire or a fairy or an elf. In fact, Bram Stoker's Dracula could go out in daylight just fine.
The real issues with Twilight lie in the fact that it not only depicts, but glorifies an abusive, controlling relationship. Edward stalks and obsesses over Bella, won't allow her to make her own decisions and forces her to do what he wants without getting her own say. This is depicted as being both normal and an ideal relationship, and if that's what interests young girls they will seek that kind of partner and that kind of relationship. It's literally dangeous, but most Twi-haters don't get that.
Also, it's not just teenagers who read it - it's also young adults and even middle-aged women. But yes, it's pretty much abstinence porn.