"match unsuitable, unfitly, or inaccurately," 1590s, from mis- (1) "badly, wrongly" + match (v.). In later use especially of marriage. Related: Mismatched; mismatching.
"a bad match, discrepancy, lack of correspondence," c. 1600, from mis- (1) "bad, wrong" + match (n.2). Sports sense of "unfair contest due to unequal abilities" is by 1954. Related: Mismatchment (1841).
prefix of Germanic origin affixed to nouns and verbs and meaning "bad, wrong," from Old English mis-, from Proto-Germanic *missa- "divergent, astray" (source also of Old Frisian and Old Saxon mis-, Middle Dutch misse-, Old High German missa-, German miß-, Old Norse mis-, Gothic missa-), perhaps literally "in a changed manner," and with a root sense of "difference, change" (compare Gothic misso "mutually"), and thus possibly from PIE *mit-to-, from root *mei- (1) "to change."
Productive as word-forming element in Old English (as in mislæran "to give bad advice, teach amiss"). In 14c.-16c. in a few verbs its sense began to be felt as "unfavorably," and it came to be used as an intensive prefix with words already expressing negative feeling (as in misdoubt). Practically a separate word in Old and early Middle English (and often written as such). Old English also had an adjective (mislic "diverse, unlike, various") and an adverb (mislice "in various directions, wrongly, astray") derived from it, corresponding to German misslich (adj.). It has become confused with mis- (2).
"one of a pair, an equal." Middle English macche, from Old English mæcca "companion, mate, one of a pair, wife, husband, one suited to another, an equal," from gemæcca, from Proto-Germanic *gamakon "fitting well together" (source also of Old Saxon gimaco "fellow, equal," Old High German gimah "comfort, ease," Middle High German gemach "comfortable, quiet," German gemach "easy, leisurely"), from PIE root *mag- "to knead, fashion, fit."
Meaning "person or thing that exactly corresponds to another" is from c. 1400. Middle English sense of "matching adversary, person able to contend with another" (c. 1300) led to sporting meaning "contest," which is attested from 1540s. Meaning "a matrimonial compact" is from 1570s.
mid-14c., macchen, "be able to compete with, be an adequate opponent for;" late 14c., "to join one to another" (originally especially in marriage), from match (n.2). Meaning "to place (one) in conflict with (another)" is from c. 1400. That of "to pair with a view to fitness, find or provide something to agree or harmonize with" is from 1520s; that of "to be equal to" is from 1590s. Related: Matched; matching.
<a href="https://www.etymonline.com/word/mismatch">Etymology of mismatch by etymonline</a>
Harper, D. (n.d.). Etymology of mismatch. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/mismatch