My 2c as a catalan speaker. Apparently cunt is related to the latin "cunnus" (wedge). We also have a vulgar word related to cunnus for vagina, "cony". Its use is not as offensive as cunt, but it is up there with "puta" (whore) as the worst things you could say to a woman. However "cony" is also used in a sexual context: "Et vull menjar el cony" could be translated to "I want to eat your pussy".

Of course we have other obscene words for vagina. One of them is "conill" (rabbit), which is apparently related to "cunniculus" (burrow). The analogy between the action of the animal when hiding and the sexual act seems clear, but however this one is almost exclusively used in descriptive contexts: "L'hi he vist el conill", "I've seen her pussy".

"Conill" is also used more innocently. A young girl (~4yo) who is playing and running around naked could be affectionately called by female relatives "conillet". "Ai el conillet!" as in "oh, the little rabbit!". The goal here, I believe, seems to be not really shaming her to get dressed, but to make her aware that she is naked.

The animal analogy (?) would be similar to that of beaver, I suppose. But of course no mother would call her naked girl little beaver.

Maybe it's just me, but I find it fascinating how languages converge and diverge, and how we find hilarious and imaginative ways to describe the world around us.