Hazel, you didn't do anything to deserve that treatment. It wasn't anything you did or anything you are. Sometimes families pick a scapegoat for abuse.
I think some abusers do this because deep down they hate themselves, and they don't know what to do with that hate. My dad is like this -- even in his hubris, when he's putting us down and puffing himself up I know he deeply hates himself. And he will pit sibling against sibling, saying how one is better than the other when in a fight with one of us. One day I'm great, one day I'm trash in his eyes.
But I know, even intellectually knowing that it's the abuser's issue and nothing to do with you, it doesn't reach the heart/belief level and it doesn't make it hurt any less. I just wanted to encourage you as I'd want someone to encourage me, by telling you is absolutely isn't your fault and you did not do or be anything wrong.