nip it in the bud
It’s a gardening metaphor. No butts are involved.
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Wrong: Let’s nip this in the butt.
Right: Let’s nip this in the bud.
Pruning a bud stops the plant growing. That’s the image.
Where it comes from
Straight horticulture, in English since at least the 1600s. You nip off a bud before it opens, and the flower never forms. Applied to a problem: stop it while it’s small.
Butt produces an image that is memorable, violent, and unrelated to stopping anything early.
This is an eggcorn—a misheard phrase reshaped into words you know. It’s a reasonable mistake to make out loud and an unmissable one in writing.
Now go prune something.