In conflicts, people rarely put up a fight to prove that a point of view is correct.
Even if they’re proven wrong, they will walk away in peace if they FEEL that they were heard, and people are leaving with the perception that THEY were correct (not whether their idea was correct–but that they were correct).
It was never about the idea—it was about them all along.
So, find a way to resolve the conflict in peace. Your team will be much better off.