Well, dogs are "man's best friend". They're automatically good guys. Even if they're vicious monsters (full disclosure: a dog killed my rabbit).
Cats deal with humans on their own terms. They don't follow orders (and don't need to to be useful as vermin catchers). They'll snuggle up to anyone who pets them because they're whores. They also are traditional companions--not to stalwart men--but women, lonely women looking for substitutes for men, and satanic witches! Also, though dogs are often brutal in their desire to chase and kill, cats are noted for their sadism regarding mice (I have a book on rabbits which states that wild cats will kill them for sport rather than food).
These images were capitalized on in Maus and An American Tail. Mice were the helpless and meek Jews, Cats were Nazis, Americans were dogs.