Not every conflict needs compromise; sometimes one side is simply mistaken.

Meeting in the middle is a good instinct and a poor universal rule. Sometimes the facts are simply on one side, and splitting the difference produces a worse answer that everybody has now agreed to. Compromise is a method for competing preferences, not for questions with answers.

Check first whether this is a matter of taste or a matter of fact. If it is fact, the work is finding out, not negotiating. Conceding half a truth to preserve the peace produces a peace built on something false.