There are a lot of people who say their cat acts like a dog, seriously. You can find quite a few vids on Youtube, e.g this cat playing fetch.
https://www.youtube.com/watch?v=nooGqHGNn1g
There’s apparently not as many dogs who think they’re cats, but at least the precedence is there on which to lay the foundation for the argument.
That’s what every cat person says when they try to convince me that I’ll like THEIR cat.