Before we engage others, we must first engage ourselves. If we do not understand our own desires, strengths and weaknesses, how are we to understand the same in others. When we see conflict, the first place we should look is in our own heart. First ask, "What might I have done to make this happen? What possible issue could someone have with my position?" If we can see things from the other person's perspective, we can better understand.
Even if, after serious introspection, we find ourselves to be in the right, the act of looking at our argument from another perspective can provide us with insight to help win the minds of others. If you can understand the conflict from the eyes of the adversary, it too can help us to understand our own desires, strengths and weaknesses.