This is partially due to main characterness. Main characters always have more screen time, deeper powers, etc, so naturally she would be the one to exhibit such traits.
The other reason is cats are cuter and cat-like behavior is easier to quantify than a bird or finless porpoise. This even happens in other shows where characters are fox-themed or tanuki or have random parts(chimera) but still act rather cat like. Only dog-themed characters have a truly distinct set of behaviors, and this seems due to the fact that people can observe and interact with dogs on a regular basis just as they have with cats.
Had all the Mews exhibited their animal traits it would have been much more entertaining.


That point when you realize you are the weird friend people talk about