“pussy” is the shortened form of the word “pusillanimous”, which means “timid, cowardly”, therefore it is saying do not be a coward.
person 1: let’s go on that roller coaster at six flags that goes in a loop!
person 2: no way that’s terrifying!!
person 1: come on man, don’t be a pussy
Don't be a pussy if the Zombie Apocalypse happens, because if you are, you will die before the first week of it ends or at least you won't last long, even if you get past the first week.