1620s, "fit of ill humor," perhaps imitative of an exclamation of disgust (cf. German muffen "to sulk").
1797, "to take offense at;" 1811, "to put out of humor," from miff (n.). Related: miffed; miffing.
To anger; offend: The way I came on to you the other night; I thought you'd be miffed (1811+)