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1530s, "fit of ill feeling," from Middle French pique "a prick, sting, irritation," noun of action from piquer (see pike (n.2)).
"to excite to anger," 1670s, from French piquer "to prick, sting" (see pike (n.2)). Softened meaning "to stimulate, excite" is from 1690s. Related: Piqued; piquing.