How do I stop taking sides when I'm supposed to be neutral?

Losing the parties' trust because you drifted to one side is a painful thing to notice, and the fact that you see it means you can fix it. Most people who take sides never realize they are doing it. You do. That is the whole beginning. You likely lean without meaning to because one side feels more reasonable, more like you, or simply easier to agree with. That instinct is human, but in your seat it leaks out in small ways: who you look at, whose point you build on, whose you gloss over. The parties feel it before you do. Catching it means watching your own small habits. So try one discipline this week. After each side speaks, restate their point back until they say yes, that is it, before you move on. Give both sides that same care, visibly. Neutrality is not something you feel. It is something you show, evenly, again and again.