You can be right, or you can fix the thing. Pick the one that still matters next week.

Being right and fixing the problem are two different projects, and they compete for the same time. One of them ends with an apology you extracted and a situation unchanged. The other ends with the thing working and nobody keeping score, which is less satisfying in the moment and the only one that is still true next week. Most arguments quietly switch from the second to the first without anyone announcing it.

When you notice you are collecting evidence rather than solving anything, drop it. Ask what the next useful step is. Being right can wait, and it usually becomes obvious anyway.