Bonus points if it’s usually misused/misunderstood by the people who say it
You don’t get tired of arguments? I see it as a ‘fine, be stupid if you want’ because I’m not spending more time on the point.
Agreeing to disagree is just more polite and often nicer for both, if such agreement is reached. You’re basically saying that we can’t really convince each other of our position so let’s just leave it at that instead of trying endlessly.
I just don’t like the phrasing because “agreeing to disagree” makes it seem like you are accepting that it’s good that they don’t agree with you. Saying literally anything else to convey what just said would make more sense.
Why do people keep acting like there’s nothing between 0 and 100? You could also say “I don’t think we’re going to convince each other in this conversation,” which is already politer, without having to ask someone to agree to something else that they don’t want to agree to.