Beef began its life as an intransitive verb in 1888 and soon took on the noun meaning in 1899 appearing in such expressions as "What's your beef? and "I had a beef with him" (not a steak).
Beef as verb  Slang (originally U.S.): To complain, gripe, grumble, protest. Hence verbal noun ‘beefing.’ Earlier it meant to talk loudly or idly.
- 1888 “He'll beef an' kick like a steer an' let on he won't never wear 'em.”—New York World, 13 May
Beef as noun  Slang (originally U.S.): A complaint, protest, grievance, gripe, objection, argument, a bone of contention.
- 1899 “He made a Horrible Beef because he couldn't get Loaf Sugar for his Coffee.”—Fables in Slang (1900) by George Ade, page 80
Regarding its origin I could find two main assumptions:
according to Etymonline it comes from American soldiers slang:
- The origin and signification are unclear; perhaps it traces to the common late 19c. complaint of U.S. soldiers about the quantity or quality of beef rations.
While this extract from Quora suggests that is origin is from rhyming slang:
- As regards the etymology of beef, it seems to go back to the cry of hot beef! meaning ‘stop thief!’ (quasi-rhyming slang but more by coincidence than design, since it is far older than rhyming slang's first widespread use in the 1820s-30s); thus the 18th century cry hot beef, to raise a hue and cry. This became ‘to raise an alarm’ or ‘make a fuss’ - the presence of crime was now irrelevant - and thence ‘to shout’. The 'complain' use followed that. Then (both in the late 19th century) came ‘to argue’, ‘to give someone away to the authorities’, and so on.
- The figurative usage of "beef" appears to be mainly and originally an AmE one, so the reference to American soldiers (and possibly cowboys) sounds reasonable, but the rhyming slang assumption would make it a BrE expression which, for some reason, became popular in the U.S., or are we talking about two different stories which originated the same expression?
In short, is there a plausible and reliable origin of the figurative usage of "beef"?
Related: Do you have a beef with me?