Why are political extremists, on both ends of the spectrum, so unwilling to entertain even the mere possibility of being wrong, about anything?

RedFever
This is not me
This is not me
I just don't get it. It's simple really. When confronted with an obvious mistake, or outright blunder, just say the following simple words: "I was wrong". There! Easy! :)
You see, this is one of the reasons why I absolutely loathe politics. There are no reasonable people to be found, with the possible (stress - "possible") exception in the centre of the spectrum somewhere.
I just recently had a little disagreement with someone who was clearly wrong about something, because it was so damned obvious to anyone who didn't have an axe to grind (like me), but oh noooo... He couldn't admit to being wrong. That was simply too much to do, too much of a sacrifice! (sigh)
Why are political extremists, on both ends of the spectrum, so unwilling to entertain even the mere possibility of being wrong, about anything?
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