Maybe it's reading a story on reddit about an entitled Karen, or maybe it's talking to an upset customer that starts to threaten you, or maybe you're expressing frustration at someone else not doing their job the way you think it should be done whether or not you're in the right for thinking such a way! I've seen and heard the term "I'll have your job!" usually referenced to them getting you ultimately fired and removed from the position.
Now, at no point have I ever noticed people expressing a desire to replace that person, or do a better job; they generally simply express that they want that person removed because of some slight against the one expressing the complaint.
How did this term come to mean getting someone fired? What's the origin of it? Is it one of those mis-heard statements that got morphed into a different meaning (i.e. "The proof is in the pudding" from "the proof of the pudding is in the eating")? Did it used to mean someone assuming they could do a better job and replace the problem employee?