Whether or not they are animals is irrelevant.
Stud, Bull, Stallion, Horse, Bear
Derogatory and also names for penis:
Cock, Pecker
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I was talking about an informal general purpose slang, which chick is. chick is similar to dude and stud. They are in different categories as far as something like bitch for instance. That being said however, I hear many women call each other bitches in a playful sense.
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I have also heard many women refer to their junk as “bird” although that’s probably pretty dated.