AIO Want to break up over a having a pet

I feel like maybe this is something I should be able to give up if I love someone, but I can’t.

I’m a massive animal person, I love them, I had a cat but my sister took him with her (she got him initially) when she got married and moved out and he’s like my best friend. I was planning on getting another cat now or whenever I move out to my own place, but my girlfriend of 3 years now is terrified of cats. She says she couldn’t live in a house with a cat in it, now I understand some people can just have irrational fears, but this is something pretty big to me. I’ve always loved cats and they bring a calming nature into the home. (Sometimes lol) I actually kind of want to break up over this.

She said she would try and work on her fear, but a couple of her friends have cats and they for some reason don’t like my girlfriend and hiss at her all the time, scaring her even more. She will flip-flop on how accepting she is on the idea.

Now am I a bad person for choosing having a pet over a partner? Or I guess deciding on finding a partner that will also be happy with getting a pet over the partner I have and love right now? I’m confused :/