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).
word-forming element of Latin origin (in mischief, miscreant, misadventure, misnomer, etc.), from Old French mes- "bad, badly, wrong, wrongly," from Vulgar Latin *minus-, from Latin minus "less" (from suffixed form of PIE root *mei- (2) "small"), which was not used as a prefix in Latin but in the Romanic languages was affixed to words as a depreciative or negative element. The form in French perhaps was influenced in Old French by *miss-, the Frankish (Germanic) form of mis- (1).
Transitive sense (as in step foot in) attested from 1530s. Related: Stepped; stepping. Originally strong (past tense stop, past participle bestapen); weak forms emerged 13c., universal from 16c. To step out "leave for a short time" is from 1530s; meaning "to go out in public in style" is from 1907. Step on it "hurry up" is 1923, from notion of gas pedal.
Etymologically, a stepfather or stepmother is one who becomes father or mother to an orphan, but the notion of orphanage faded in 20c. and came to denote simply relation through marriage. For sense evolution, compare Latin privignus "stepson," related to privus "deprived." Compare orphan (n.).
Lock-step. A mode of marching by a body of men going one after another as closely as possible, in which the leg of each moves at the same time with and closely follows the corresponding leg of the person directly before him. [Thomas Wilhelm, "Military Dictionary and Gazetteer," Philadelphia, 1881]
Figurative use by 1836.