DuckDuckGo search for “pusillanimous meaning”, 2nd definition from the top.

> Destitute of a manly or courageous strength and firmness of mind

Not much of a leap.

I guess because it’s a snobby way of saying “they weren’t pussies about it”

You've guessed wrong.

The etymology is latin for "small (pussilus) spirit/courage (animus)" meaning "faint of heart".