The root
definition of Pussy is "soft and fuzzy". You can replace the word Pussy in just about any context with the words soft and fuzzy.
Pussy Cats are soft and fuzzy.
Pussy Willows are named
after the soft and fuzzy buds on thier branches.
Cowerdly people are not hardened, so soft. (However not always fuzzy)
A womans pussy or vulva is also soft and sometimes fuzzy.