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1610s, "a pun, a play on words," probably a diminutive of obsolete quib "evasion of point at issue," based on an overuse of Latin quibus? in legal jargon, which supposedly gave it the association with trivial argument. Meaning "equivocation, evasion of the point" is attested from 1660s.
"equivocate, evade the point, turn from the point in question or the plain truth," 1650s, from quibble (n.). Earlier "to pun" (1620s). Related: Quibbled; quibbling.