"So... Do they feel let down? were you not there for them in an hour of need? Did you show disrespect for their values, what they stand for, or who they are? Did you talk about them to other people? Break a confidence? Did you treat them unfairly? Punish them or someone else for something which was not their fault, or just a mistake? These are all yhings which I think a child of mine might ferl justified to feel hate for me, and I should apologise for if I did them, even unintentionally or thoughtlessly."
Um, no.
I don't think it's justified to hate someone who hasn't been a perfect person or a perfect parent. Someone who has made mistakes because, you know, they're HUMAN.
Teenagers hate their parents - mostly - because they are teenagers, and they are going through a process of separation which sometimes manifests itself as strong and irrational feelings of antipathy towards people who love them.
OP - I have been through four years of this with dd. A few months ago she calmly told me that she wanted to cut my throat. She has also told me she hopes I get cancer. 
Miraculously she has simply stopped doing it over the space of about 4 weeks. I haven't changed, she has. I now get 'I love you' and hugs every day. She is 16.
Sadly, ds1 (12) is horribly hormonal and she has passed the hateful teenager baton along to him so I've had 'I hate you' this week from him. I'm horrible and vile because I ask him to tuck his school shirt in, ask him to do his music practice and homework, make him go to bed by ten, and get him put his plate in the dishwasher. I'm cruel me!