I’m curious what the alternative to “agree to disagree” is.

Agree to agree? Refuse to agree? Refuse to disagree?

Either you convince someone to change their mind or you don’t. If you don’t convince them then you either keep trying past the point where it is clearly futile or you stop trying. If both sides of a disagreement stop trying then they’ve agreed that they disagree.

Oh! I did think of an alternative. You could pretend to agree and secretly disagree. Is that what you are suggesting is preferable?