Parties to a dispute can feel prideful, threatened, or just plain right about the case. Sometimes, it’s the last one that’s the problem.
In Botond Koszegi’s 2006 article “Overconfidence, Ego Utility and Task Choice” (link), he uses decision theory to demonstrate the dissonance between peoples’ chronic overconfidence and their constricting risk aversion. In short, people need to see themselves as successful, and to erect a forcefield around that vision:
The model starts from a simple premise: People have ego about what activity they see themselves capable of succeeding in… In addition to caring about financial outcomes, a person might derive pleasure from thinking that she belongs to the distinguished group of people who could have a successful business.
When ego rules, parties view themselves as right and others as wrong, regardless of what anyone is saying or what the facts are. When ego is an issue, deflecting the source of a settlement offer away from the temporarily hated opposing party may be prudent. Similarly, allowing a party to exercise self-agency in resolving a dispute may save the self-image of a party that is terrified of having that image shattered, whether the party is conscious of that terror or not.