I would guess that @Fiddle_Playing_Creole_Bastard has the derivation right. I tried the UrbanDictionary.com which often gives the derivation of such slang, but they didn’t provide any clue how this one came into common usage. They did, however provide a clever definition of how the meaning changes as each of us gain savoire faire:
Definition 4: Pussy.
1. Obvious to anyone over 1 year old
because they want to pet it
2. Obvious to anyone over 8 years old
because they want to make fun of them
3. Obvious to anyone over 12 years old because they want to make fun of it, but also stare at it, pet it, put stuff in it etc.
Usage:
1. 5 year old: I want my own pussy cat
2. 10 year old: Stop being a pussy
3. 18 year old: Wear this shirt to the club, you`ll get finer pussy than you thought exists :