One thing I have learned, not in the dojo, but as a nurse and a family member, is that "being right" isn't always the most important thing. How we comport ourselves among others is.
Here is a quote I found from a book on cross-cultural rhetoric. The quotation is from a life of the Buddha. He is being pressed by opponents with questions as to whether he would ever use unpleasant, disagreeable speech. He replies,
"Speech that the Tathagata knows to be untrue, false, and useless, and also unpleasant and disagreeable to others, he does not speak; that which he knows to be true, real and useful, but also unpleasant and disagreeable to others, he knows the right time to express it. Speech that he knows to be untrue, false and useless, and also pleasant and agreeable to others, he does not speak; that which is true, real, but useless, and also pleasant and agreeable to others, that, too, he does not speak; but that which is true, real, and useful, and also pleasant and agreeable to others, in that case he knows the right time to express it." (Edward J Thomas, The Life of Buddha as Legend and History
So, for the Buddha, timing is everything. This is part of an Indian rhetorical tradition that is definitely not Greek. The rhetorical tradition that is usually called 'western' is based on ancient Greek rhetoric, which itself is based on contentious disputation prior to a decision being taken by third parties.