late Old English hyttan, hittan "come upon, meet with, fall in with, 'hit' upon," from a Scandinavian source such as Old Norse hitta "to light upon, meet with," also "to hit, strike;" Swedish hitta "to find," Danish and Norwegian hitte "to hit, find," from Proto-Germanic *hitjan, which is of uncertain origin. Meaning shifted in late Old English period to "strike, come into forcible contact" via the notion of "to reach with a blow or missile," and the word displaced Old English slean (modern slay) in this sense. Original sense survives in phrases such as hit it off (1780, earlier in same sense hit it, 1630s) and is revived in slang hit on (1970s).
To hit the bottle "drink alcohol" is from 1933 (hit the booze in the same sense is from 1889, and hit the pipe "smoke opium" is also late 19c.). To figuratively hit the nail on the head (1570s) is from archery. To hit the hay "go to bed" is from 1912. Hit the road "leave" is from 1873; hit the bricks is from 1909, originally trade union jargon meaning "go out on strike." To hit (someone) up "request something" is from 1917. To not know what hit (one) is from 1923. Related: Hitting.
miss v.
Old English missan "fail to hit, miss (a mark); fail in what was aimed at; escape (someone's notice)," from Proto-Germanic *missjan "to go wrong" (source also of Old Frisian missa, Middle Dutch, Dutch missen, German missen "to miss, fail"), from *missa- "in a changed manner," hence "abnormally, wrongly," from PIE root *mei- (1) "to change, go, move." Reinforced or influenced by cognate Old Norse missa "to miss, to lack." Related: Missed; missing.
Sense of "fail to find" (someone or something) is by late 12c. Meaning "fail to note, perceive, or observe" is from early 13c. Meaning "fail to reach or attain what one wants" is from mid-13c. Sense of "perceive with regret the absence or loss of (something or someone)" is from c. 1300. Meaning "omit, leave out, skip" is by mid-14c. Sense of "to escape, avoid" is from 1520s.
Sense of "to not be on time for" is from 1823; to miss the boat in the figurative sense of "be too late for" is from 1929, originally nautical slang. To miss out (on) "fail to get" is by 1929.