Getting fired, unceremoniously, and at a point in time you don't control, is quite a different thing from a planned exit where you already have your new position lined up and waiting. I propose that "correcting" your boss is likely to lead to the former, which is bad, and that - IF one cares so much about this point - it is better to just go ahead and start planning the latter.

Edit: I should perhaps have been more explicit in saying that I meant "start looking for a new job so you can quit" as opposed to "rage quit on the spot".