Do you have a beef with me?

To have a beef with somebody/something means:.

• to think someone or something should be changed.

  • I've got nothing against advertising, but I do have a beef with how many bad ads there are on TV. (Cambridge Dictionary)

Is it more British or US in usage? But mostly, where does this "beef" come from?

Solution 1:

OED doesn't have much in the way of definite data:

noun
4. A protest, (ground for) complaint, grievance. slang (orig. U.S.). Cf. beef v. 4.

1900 G. Ade Fables in Slang 80 He made a Horrible Beef because he couldn't get Loaf Sugar for his Coffee.

verb
4. intr. To complain, grumble, protest. slang (orig. U.S.).

1888 N.Y. World 13 May (Farmer), He'll beef an' kick like a steer an' let on he won't never wear 'em.

It would appear that cattle were known for being ornery and not afraid to complain about something they didn't like, and the term beef migrated to have that meaning.