Is it normal that i truly hate my mother?

I think my mother is a sociopath, or at least a very cold person. Every birthday that was supposed to be happy or at least fun, was always turned into something humiliating or depressing. On my 7th birthday, i got too excited for her patience and was sent to my room while my siblings and friends got to enjoy the party. She left the door open so that i could hear them laughing and enjoying the fun. On my next birthday, she made a big show out of giving my siblings really cool presents and giving me a sweater. Every time i did something that that annoyed her she would say that i was just like my father and would never be anything (though in adulthood, ive been the most successful in terms of financially of my whole family). When i told her i was sexually abused at age 9, her exact words were " you need to learn to fight back". There is of course more, but i think you get the jist at this point.

I truly hate her. When i heard through relatives that she had been diagnosed with lung and breast cancer, i felt my heart pound and im sure my eyes lit up. She lived through the cancer, however.

I have completely written her out of my life and have no desire to make amends or to give her another chance.
I guess what im really asking is has anyone else had this kind of relationship with a parent, one so toxic that you feel the need to cut off all ties to them? Responses are appreciated.