Etymologically, it seems like there are theories surrounding where it comes from.
The ones I'm familiar with are 'poesje', a Dutch word meaning 'little cat'. The other is the Old English word 'pus' meaning 'pocket'.
I'm far more inclined to believe 'poesje' is the origin, with 'pus' being an incorrect association due to common modern usage of the word 'pussy' in place of 'vagina'.
Idk who convinced this guy that it's short for pusillanimous. Sounds like someone trolled the fuck out of him. Anyone with a strong understanding of English (and language, really - what I'm about to say is just human nature) understands that languages follow the path of least resistance. It, logically, does not make sense that pusillanimous (a word totally unused in the average English speakers vernacular) would be where pussy comes from. Unless your inner idea of English speakers 3 centuries ago is some fucked up Shakespeare-an parody.
There's a marked difference, though, the Moon can't actually generate words that you can digest. Some people might think the Moon is speaking to them, but their brains are just spicy - it is not the same as a machine.