The person retelling an argument controls how reasonable everyone sounds afterward.

Whoever tells the story afterwards is doing the editing, and editing is where most of the fairness lives. The retelling keeps your own hesitations and drops theirs, keeps their sharpest sentence and drops the one that provoked it. This usually happens without dishonesty, because memory hands you your own reasons and only their behaviour. The listener then ends up judging a version rather than an event.

Next time you describe a disagreement, include one line the other person said that you found hard to answer. It costs very little, and it keeps your account from quietly becoming a case.