Listen or thy tongue will keep thee deaf. Native American Proverb
I don't know about you, but I find the balance between advocating for my idea versus considering an alternative opinion to be a difficult balance to maintain. It requires two distinctly different and demanding cognitive tasks. First, there is a practical need to formulate an argument and the evidence to maintain it. Second, there is the need to hold the argument back while considering alternatives. I need to be certain of my idea while at the same time consider that perhaps my idea isn't the best. I, and many leaders I know and have known, find this nearly impossible.
Making this balance even more difficult is the issue of passion. If a leader isn't listening only because he or she doesn't want to "lose" the argument, that's bad enough (and sometimes impossible to resolve). However, the issue often is that the leader cares so much about the topic that the debate is really about emotion rather than cold hard facts. When the argument appears to be factual, but is actually emotional, it can take a long and messy conversation to sort it out. If this conversation occurs in a group rather than one-on-one, it becomes even messier.
Consider the latest (or current?) conflict of opinion in which you are involved. It might be that you're not the only passionate one in the debate. If that's the case, consider the shared passion to be a point of agreement. Then, stop talking. It might be that the passion of the other person, whether another leader, subordinate or peer, might lead them to a better solution than the one you are advocating. Maybe not, but it's at least worth a little silence.