I have a friend who thinks I have offended her. I disagree. She is now demanding an apology. If I refuse, she is threatening to walk out of my life forever. I would prefer that does not happen, despite this conflict. What should I do? Should I apologize even though I do not mean it?

This is an important dilemma, whether to choose truth or friendship. I recommend that you choose both. If it were me, I would tell the truth this way, “I am sorry that I hurt your feelings for [then state what the issue is].”

I am presuming that you wish she was not hurt by whatever she thinks you did. You would be acknowledging this. You are not apologizing for a supposed injustice that you say you did not commit.