Is it normal to hate your own mother?

Okay, so from the age of about 3, I prayed that one day someone would tell me there was a mix-up at birth and my mother wasn't actually mine. I've hated her for as long as I can remember. I can't even bring myself to lie and say "I love you." I was never physically abused or anything like that, but she has mentally destroyed me. All the dreams I had, she'd tell me "You'll never manage that", "you can't do it". She has called me every single bad name under the sun. Not all that long ago she said to me "I have hated you since the day you were born." I will never forget that. I have an unfathomable hate for her. I can't even look at her without my blood boiling, my chest tightens and I feel sick to my stomach. All I ever asked from her was some emotional support, but she can't give me that. I don't care for her, or her attitude. She has failed me, and I have 2 younger siblings I'm concerned about. It worries me to think they might be treated the same way. I worry that she tries to destroy them too. I don't want them to have their confidence ripped from them like I have. Can someone please explain to me why she is like this?! And what I have done from such a young age, to be treated like this?