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1560s, "clasp, interlock," especially with a bent nail, variant of clench. The sense of "settle decisively" is first recorded 1716, from the notion of "clinching" the point of a nail to keep it fast. Boxing sense is from 1860. Related: Clinched; clinching.
1620s, "method of fastening," from clinch (v.). Meaning "a fastening by bent nail" is from 1650s. In pugilism, from 1875.
[fr the bending over, clinching, of the point of a nail to ensure it does not pull out; ultimately fr clench]