Isn't it interesting how everyone takes different meaning from words? I would never associate it with a cat, but only with anatomy when used in a derogatory manner. While I read quite a bit, I can't say I have ever read or looked into the origin of phrases. When I come across them randomly, I think it's quite fascinating.
When we had cats we actually named them Puss...Black Puss, Ivy Puss, Big Puss, ha ha! My son got in trouble at school for saying the name of his cat. Needless to say, we had a talk with his teacher about how she shouldn't teach young children meanings of bad words when they think it just means a cat.