Many disputes go beyond facts and are not clear cases of "you were right and I was wrong." All too often there is some justice on both sides. But if we are able to concede our shortcomings in factual disputes, that will extend to other areas of disagreement. And it means that our attempts at peace will be based on a shared and mutually accepted reality rather than our partisan perspective. Even if it hurts at first, saying, "you were right and I was wrong" is just like any ethic or exercise: the more you do it, the more you can do it. We can all use a more flexible "concessional muscle"; the less you use it, the harder it is to move, in any direction or circumstances.
To make peace, we must be willing to speak peace, and acceptance, and understanding. And practice makes better, if not perfect.