The word 'hawk' descends from Old English 'hafoc' (hawk), from Proto-Germanic *habukaz, a word found across all the Germanic languages: German 'Habicht' (goshawk), Dutch 'havik,' Old Norse 'haukr,' Norwegian 'hauk,' Swedish 'hök,' and Danish 'høg.' The Proto-Germanic form is sometimes connected to PIE *kap- (to seize, to grasp), which would make the hawk 'the seizer' — a bird named for its predatory strike, the moment when talons close around prey. This same PIE root, if the connection is sound, produced Latin 'capere' (to take, to seize), the ancestor of 'capture,' 'captive,' 'capable,' 'accept,' and 'receive.'
The Old English form 'hafoc' shows the word before the loss of medial consonants that produced the modern clipped form 'hawk.' The compound 'gōshafoc' (goose-hawk) survives as 'goshawk' — a large hawk powerful enough to take geese. The sparrowhawk (a hawk that hunts sparrows) preserves the naming convention of identifying hawks by their prey.
Falconry — the practice of hunting with trained birds of prey — was one of the defining aristocratic pursuits of medieval Europe, and it generated a rich specialized vocabulary. Technically, 'hawk' and 'falcon' denote different families of birds (Accipitridae and Falconidae), but in the language of medieval falconry, the terms carried social distinctions. The Boke of St. Albans (1486) famously assigned different raptors to different social ranks: an eagle for an emperor, a gyrfalcon for a king, a peregrine for an earl, a goshawk for a yeoman, a sparrowhawk for a priest, and a kestrel for a knave.
The political sense of 'hawk' — an advocate for aggressive, militaristic policy — originated during the War of 1812. American politicians who pushed for war against Britain, led by Henry Clay and John C. Calhoun, were labeled 'War Hawks' by their opponents. The opposing metaphor, 'dove' (an advocate for peace and diplomacy), followed naturally, with the dove's biblical association with peace (the dove returning to Noah's Ark with an olive branch). The hawk-dove dichotomy
The verb 'to hawk' (to sell goods aggressively in the street) is unrelated to the bird. It comes from a Low German word 'höken' (to peddle), related to 'huckster.' The homophony is coincidental. However, 'to hawk' meaning 'to hunt with hawks' is directly from the bird, and 'hawking' as a synonym for falconry preserves this sense.
Hawk imagery pervades English idiom. 'To watch like a hawk' means to observe with intense, predatory attention. 'Hawk-eyed' means sharp-sighted. 'Hawkish' describes an aggressive policy stance. The surname Hawkins means 'son of the hawk,' and Hawking (as in Stephen Hawking) shares this origin.