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I’ve thought about this at length and the conclusion I’ve reached is that people tend to lose ‘authority’ when they admit they’re wrong on a subject.
Essentially, once you’ve believed something that was incorrect, your peers will be more skeptical of your beliefs in the future and they can always point back to “remember when you were wrong about x?”
The stronger you’ve held this incorrect belief, the harder it is to admit you were wrong.
If they never admit they were wrong, though, then they never have to deal with humiliation.