Homonyms do sometimes have completely unrelated etymologies, like with the word “Pussy” meaning coward, and being a slang term for the vulva. The cowardly definition came from a shortening of the word “Pusillanimous,” while the slang term came from women being compared to cats.

"Pussy" in the sense of "female genitals" is more likely related to "purse", referring to the vagina's pocket-like shape; and "pussy" in the sense of "weakling" is either ordinary misogyny or a reference to a kitten's helplessness.

(And "pussy" for an actual cat is related to words for "cat" in some other European languages, like Romanian pisică; which ultimately come from the pss-pss call that is effective at getting a cat's attention.)

If you want a funny etymological example though, take a look at the word "cleave". In modern English it has two opposed meanings: "cling together" and "split apart". This is because it was two different verbs in Old English, cleofan (the "split" meaning, related to "clove" and "glyph") and clifian (the "cling" meaning, related to "clay" and "glue")!