“Pussy” meaning “female genitals” is the most recently coined usage. Its meaning as “timid and cowardly” really did come about earlier, referencing the skittish nature of pussy cats. (Some people believe it comes from “pusillanimous,” which is also plausible but less well-supported.)
It would be more logical to push against using pussy to mean vag, but that’s probably a quixotic lost cause.
