It's ok for her to not like cats. But yeah, it's not so cool to be continually insulting yours.

Have you been together quite a while? Like is it a fairly serious relationship? It might be worth considering the future right now - if the two of you ever got serious enough to consider living together, will she be ok with the cat there or will she try to make you get rid of it? You might want to make it clear that your cat is there to stay. i would never get rid of my pets - the only way I'd rehome them would be if I had a baby who was allergic - and even then it'd have to be a serious allergy.