Is it okay if I want to give away my mom's cat?
Why would you want to rehome the cat from your mother?
It's a cat, I'm allergic to it. I don't want to adopt a new cat
It's fine for you to personally give up your own pet if you cannot care for it, but this is your mothers. You should talk to her about your concerns and if she agrees then you could give it to a nice new home, but if she wants to keep it then you need to find a solution for yourself because abandoning a pet is wrong.
You're a close minded asshole that only cares about that bitch cat.
Would you feel the same way if it were your own pet? Your mother loves her cat and would be very sad if you were to take that from her. There are ways for you to try to acclimatize your allergies with animals, so you could try that.