c. 1300, "an ox, bull, or cow," also the flesh of one when killed, used as food, from Old French buef "ox; beef; ox hide" (11c., Modern French boeuf), from Latin bovem (nominative bos, genitive bovis) "ox, cow," from PIE root *gwou- "ox, bull, cow." Original plural in the animal sense was beeves.
"to complain," slang, 1888, American English, from noun meaning "complaint" (1880s). The noun meaning "argument" is recorded from 1930s. The origin and signification are unclear; perhaps it traces to the common late 19c. complaint of soldiers about the quantity or quality of beef rations.