That parental notification law seems like it would have universal support. I'm not sure why it doesn't. I don't tell any woman or man how to raise their kids, they don't tell me how to raise mine.
I should think our objection to parental notification should be obvious - to protect the young woman from her family. The great majority of parents in America would be somewhat abusive in a situation like this - recriminations, verbal abuse, character assassination, dimunition of self-esteem, and in many cases physical beatings would be the inevitable result. It might even reach the disasterous extreme of preventing the abortion from taking place.
No, to my mind the parent is basically a tyrant, and is as often, or more often, the enemy of youth than the benefactor. I should like to protect the young woman from having to deal with the parents in this situation - simply put, if they were decent, non-abusive, open-minded, liberal parents, she would've already informed them of her own volition!