Apologizing first isn’t losing the argument. It’s being the grown-up before the other person figures out how.

Waiting for the other person to move first turns a disagreement into a contest about who can hold out longer. Going first does not concede the facts. It just ends the standoff and returns you both to the actual problem, which is usually smaller than the silence around it.

Apologize for your part specifically rather than for the whole event, and leave out the clause that explains why they made you do it. A short message works. If they do not meet you there, you have still stopped paying rent on the argument.