I believe (if my dictionary is anything to go by) that the word pussy started off a long time ago in old English to mean a pouch or a purse and evolved into it’s more vulgar meaning relatively late. I can see how a word for pouch can turn into a word for female genitalia, but how did cats and willows get involved?
Puss starts off as a “conventional” name for a cat, in print from before 1530. It is most likely a sound that was used to call a cat–i.e. “here, puss, puss!”
It appears as a name for a cat in other Germanic languages, pus and pus-katte in Low German, puse in Norwegian, poes in Dutch.
It shows up in 1726 as pussy , diminutive of puss. It shows up even earlier (1605) referring to Dick Whitington and his “pusse.”
The use of “pussycat” appears in print in 1805 in a nursery rhyme–“pussycat, pussycat, where have you been.” No doubt it was a common useage well-before that time.
It probably was turned into pussycat merely to make nursery rhymes flow more smoothly. Sing-songy kind of thing.
My info is from the OED and Chambers.
I always figured that pussy was more to do with furryness like ‘beaver’ is now… not purse…
Surprisingly Merriam-Webster drew a blank on this one, but my desk dictionary (Collins English) has this:
puss (pus) n. 1. an informal name for a cat. 2. Slang. a girl or woman. 3. an informal name for a hare. [C16: related to Middle Low German pûs, Dutch poes, Lithuanian puz ]
“Pussy” is cross-referenced to that. My WAG would have been imitative (what noise do you call a cat?). Pussy willows get their names from the resemblence of the dangling flower bracts (i.e. catkins) to cats’ tails.
Q. What animal can fly highest?
A. A flight attendant’s pussy.