Some people are genuinely afraid of cats, just as some people are with dogs.
So is she reacting out of fear, or does she only make these remarks when your paying attention to the cat and not her?
Just wondering if she could be jealous. Which would be a bit of a red flag, but nothing you couldn't talk through if she is willing. She might be embarrassed that she is jealous, so makes nasty remarks to mask it.
Same if she is genuinely fearful.

However if she just isn't an animal person, and refuses to see that her comments are hurtful to you I would be inclined to give the relationship a good hard look.
Because ultimately this speaks of something deeper than just not liking your cat.

Good luck, really hope you can work things out.