It's not all that important. In fact it's when you're wrong that you (learn) something.
Too much focus on winning an argument is a sign that people are thinking in terms of (YOU & ME) and not (US & WE).
When one habitually cares more about proving their mate is wrong then they do about being happy I'd say that's a "red flag".
"Making love beats having a war!" - Richard Pryor :-)