This is the way I see it.
Disagreements can occur because one or both parties has their facts wrong. Provided that those facts are objectively demonstrable and both parties are rational, the disagreement ought to be resolvable. But if you are dealing with someone who will not acknowledge an established fact then you may as well end the discussion right there.
Disagreements can occur because one or both parties has their logic wrong. This type of disagreement, too, ought to be resolvable, but in practice is often not. We may not like to admit when our facts are off, but we hate to admit when our logic is off. If you are dealing with someone who will not acknowledge a logical error then you may as well end the discussion right there.
If both parties agree on the facts, and neither is making a logical error, then the basis for disagreement is probably due to evaluations inferred not only from knowledge but from subjective perceptions. When all the variables of a situation are not known, we fill in the blanks with guesses based on personal wisdom, experiences, impressions, prejudices.
This is the type of disagreement by which the teenager rejects the parent’s decree of not being allowed out alone past curfew. The parent cannot tell the future, cannot say for certain that were the teenager to go out late anything would happen that would justify prohibiting him or her from having this little fun, but instead makes an evaluation that draws from personal wisdom and experience. The teenager, having a different set of wisdom and experience, makes a different evaluation.
This is also the type of disagreement by which most arguments of a political nature occur, as the consequences of any given policy are never truly known before it has been implemented, and even afterwards there are far too many variables for any one person to process thoroughly. Consciously or not, we fill in all sorts of blanks by making subjective inferences. Needless to say, some people go to greater lengths than others to obtain as much objective data as they can so as to avoid having to do this as much as possible.
When the basis of disagreement is this last type, further discussion may or may not bring about a resolution. The manifestation of additional facts at some later date might be enough to settle it, but you can never really count on that. Don’t underestimate people’s resistance to replacing their impressions and prejudices with objective facts.