For present purposes, "disagreement" is the condition we frequently find ourselves in of accepting what somebody else rejects and rejecting what they accept. Disagreement is something more than sheer difference: it requires that both parties be referring to the same thing, that there be something (an object, a proposition, etc.) on which they have taken opposing stances. If you and I are just different, then there's little more to say. But if we differ about something, then various kinds of conflict begin to look inevitable.
There are two kinds of misunderstanding that might be at the root of disagreement. One kind is the misunderstanding people have of each other: it could turn out that, every time we reject someone else's position, deeper analysis reveals that we have not rejected their position at all, but a position invented by ourselves whose sole purpose is to be rejected by us. We are perpetually on the lookout for straw men, since it is by contrasting ourselves with others that we define our own identity. If disagreeing with someone requires saddling them with a position they don't actually hold, then the better we understand the person, the less we will find ourselves in disagreement with them.
The second potential misunderstanding is a misunderstanding of what it implies for there to be multiple real takes on something. On the assumption that there are objects or propositions under dispute, what do we make of there being a plurality of views concerning them? It is easy to fall into see-sawing between two extremes: a dogmatic or absolutist extreme, whereon only one view of each thing is the correct view, and a radically pluralistic or relativistic extreme, whereon every perspective is right in its own way. It is not always noticed that the relativistic extreme entails not only that all perspectives are right (by their own lights), but also that they are all wrong (by each other's). Are we presented with a choice between one-sided dogmatism and the befuddling spectacle of always being right and wrong at the same time?