Degree Of Confidence
It is possible to try to settle a dispute in a number of different ways, all while avoiding the necessity of acknowledging that one was in the wrong regarding the nature of the dispute itself. It requires a certain amount of confidence, albeit the kind that is frequently misplaced, but overall it is still necessary.
The individual who is attempting to save face by leaving is completely mistaken in the sense that he is stating that he does not agree with cold, hard facts. A significant number of individuals have the propensity to ignore factual information if it contradicts what it is that they have been stating.