I saw your response, "Since the church isn't the building, you can't make rules about how the building is used," to an older woman who “dared” to say what is in her heart. What disrespect you showed her! Do you really believe she was open to your answer? Did you show her the wrong in her position with gentleness? No, you did not! You should apologize, and then beg God’s forgiveness.
A casual scan of this web site should show that I am not bothered by disagreements. Yes, I did dare to disagree with an older woman who thought that because her husband was a preacher that it meant she knew what she was talking about. I pointed out that she approached the discussion too emotionally and I gave scriptural justification for each point I made. Using Solomon's advice: "Do not answer a fool according to his folly, lest you also be like him. Answer a fool according to his folly, lest he be wise in his own eyes" (Proverbs 24:4-5), the tone of my reply was firm but milder than the one she presented to me.
You did not prove that the answer was wrong. You merely didn't like the way it was presented. I wonder if you would have scold John the Baptist (Matthew 3:7) or Jesus when he spoke to the Canaanite woman (Matthew 15:22-28). One style of response does not fit all people.
I have no idea if she was open to the answer. I suspect from the tone of her original note and her lack of response to my reply that she already had her mind made up. Any answer that disagreed with her position would have been rejected.
So, no, I do not apologize for demonstrating that someone is taking an incorrect position. She was promoting a false idea and I did as I must to rebuke her for that position. "Speak these things, exhort, and rebuke with all authority. Let no one despise you" (Titus 2:15).