pigeon-wing n.

late 14c., pijoun, "a dove, a young dove" (early 13c. as a surname), from Old French pijon, pigeon "young dove" (13c.), probably from Vulgar Latin *pibionem, dissimilation from Late Latin pipionem (nominative pipio) "squab, young chirping bird" (3c.), from pipire "to peep, chirp," a word of imitative origin. As an English word it replaced culver (Old English culufre, from Vulgar Latin *columbra, from Latin columbula) and native dove (n.). 

The meaning "one easily duped, a simpleton to be swindled" is from 1590s (compare gull (n.2)). Pigeon-hearted (1620s) and pigeon-livered (c. 1600) are "timid, easily frightened." A pigeon-pair (by 1800) are twins of the opposite sex (or family consisting of a boy and a girl only), so called because pigeons lay two eggs, normally hatching a male and a female.

late 12c., wenge, "forelimb fitted for flight of a bird or bat," also the part of some insects resembling a wing in form or function, from Old Norse vængr "wing of a bird, aisle, etc." (cognate with Danish and Swedish vinge "wing"), of unknown origin, perhaps from a Proto-Germanic *we-ingjaz, suffixed form of PIE root *we- "blow" (source of Old English wawan "to blow." Replaced Old English feðra (plural) "wings" (see feather). The meaning "either of two divisions of a political party, army, etc." is first recorded c. 1400; theatrical sense is from 1790.

The slang sense of earn (one's) wings is 1940s, from the wing-shaped badges awarded to air cadets on graduation. To be under (someone's) wing "protected by (someone)" is recorded from early 13c. Phrase on a wing and a prayer is title of a 1943 song about landing a damaged aircraft.