I encounter that all the time especially on public forums like this. This is a quote from an article I found about it online: According to psychologist, speaker and author Guy Winch, most people who consistently refuse to admit they're wrong do so because they have incredibly fragile egos. They clam up and insist they're right, demonstrating what experts term "psychological rigidity", as a defense mechanism.
Also I think that telling someone they are wrong comes across as a criticism about their intellect and they respond defensively by instinct. And, another reason is because people don't want to believe anything that contradicts their preferred view of the world. So if you "correct" someone they tend to act like you're attacking them or as too stupid to know what "truth" is.
It's really a telling distinction because today, most people behave in this defensive way. You don't see many people willing to concede or say, "wow that's a different point of view than I have considered, maybe it requires me to spend some thought on why I feel the way I do." Which is the real value of differing opinions; they help us re-assess and redefine the reasons why we feel the way we do.