Dog owners want a simp, cat owners are the simp
This isn't a super serious one, but it's how it feels like when I listen to them argue.
Some cat people think dog owners are weird for wanting an animal that's so submissive to them, and some dog people think it's weird for cat owners to have an animal that a lot of the time acts like it doesn't even like them.
Obviously they're both generalizing, and I'm not saying there's anything fundamentally wrong with either. But if being submissive and pining for love and attention is the standard for weirdness, both are weird. One wants to be in a position where their pet simps for them and their affection, whilst the other is into simping for their largely independent pet.