I'm reminded of the axiom, do you want to be right or kind?
Sometimes it's better to demure to another in a disagreement, which is to say that we can think from an unattached or neutral perspective and look in upon a situation, as if we are part of a camera crew filming the event for later interpretation/post introspection.
Likewise, as in your experience today, being able to remain someone detached to an unexpected or spontaneous exchange while in the moment, allows perhaps, for a kinder or gentler response than might come from a gut reaction.
I guess I'm trying to say that ya' dun' good!