Utterly Mad

Welp, I was playing Freerice.com guessing word definitions and I found an interesting one.
Pusillanimity, it means cowardice. Now I am curious if this is the origin of why we call someone who is a coward a pussy, other then it being a vulgar word for female genitalia; or is it that pusillanimity is itself derived from the word pussy.
#I probably shouldn't ramble when I am this tired.