Also, see the response about the spanish usage of 'gata'
edit: this is much too serious of a response to this funny of a thread, I should throw some humor in here somewhere ;)
It can mean, for example, variations on "Don't be so timid", "Stop expressing your fears", and "Take more risks".
Indeed, I have heard "Don't be a bitch" be used in almost the exact same way.
So when you call somebody a 'pussy' for not having the courage to do something that has _nothing_ to do with felines or vaginas. (As most people commonly seem to think). Being a 'pussy' is short for 'pusillanimous', nothing to do with cats at all…
As a side note - I've particularly become interested in the negativity of "dog" after trying to trace the origin of the proverb "The Dogs Bark but the Caravan Moves On", which is pretty common in my language (not common in English). Was surprised to find out it originated in Arabic and found it's way to many other languages.