Not every conflict should end with agreement; some should end with understanding.

There are differences that will not close, and pretending otherwise produces a false agreement that neither person believes. Understanding is the achievable end: knowing exactly why they think what they think and being known in return.

Give yourself permission to finish a conversation without a conclusion. Say that you see where they stand and you still see it differently. That is a real ending, and it holds better than a consensus manufactured to end the discomfort.