Etymology

square peg in a round hole

Today it means: Someone or something that does not fit well or at all in a certain setting; a misfit; hence, someone or something that will not succeed in an endeavour, except possibly with much effort and force. Full definition →

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The story

Commonly associated with a shape sorter, a baby toy that consists of (often wooden) pegs that need to be inserted through holes in a box, using the hole that has the same shape as the peg. While all the shapes are of roughly equal size, each peg will only fit in the hole that has the same shape. Inserting a peg in a different hole would require either modifying or breaking the toy.

Etymology from Wiktionary, CC BY-SA 4.0.