Ironically you're calling out a weird prejudice by showing your own weird prejudice
Are there not plenty of reasons not to like women? (Also men but that's offtopic)
There’s plenty of reasons not to like dogs as well.
Honestly, it's not even necessarily about not liking dogs. It's about "I'm OK with dogs but that means all our plans would have to fit into his having a dog." Nothing wrong with that, but implication of a lot more buy-in than with a cat generally.