- Old English steop-, with connotations of "loss," in combinations like steopcild "orphan," related to astiepan, bestiepan "to bereave, to deprive of parents or children," from Proto-Germanic *steupa- "bereft" (cf. Old Frisian stiap-, Old Norse stjup-, Swedish styv-, Middle Low German stef-, Dutch stief-, Old High German stiof-, German stief-), literally "pushed out," from PIE *steup-, from root *(s)teu- (see steep (adj.)).
Etymologically, a stepfather or stepmother is one who becomes father or mother to an orphan, but the notion of orphanage faded in 20c. For sense evolution, cf. Latin privignus "stepson," related to privus "deprived."