I would apologize just to acknowledge that if i had done anything wrong (even when I don’t think that I have) I didn’t mean to or that it was not intentional or could have been an accident.
Sometimes Continuing to try to prove you are right becomes a moot point or a stalemate if the other party refuses to see your side or thinks they are right.
Apologizing for me is an attempt to stop the discussion if it is not going anywhere.
You are welcome, Anthony! I don’t like to argue but when I am right I don’t like to back down either. Sometimes however, there are those people who won’t concede and at that point, it just isn’t worth it to continue to argue.

Hi Jill Dirksen,
Well said,
that is so true!
Thank you so much I really appreciate
you’re answer.