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Many people would be willing to admit that they’re wrong, however, if the “opposing” side is constantly mockign and ridiculing you, yeah, I can see why people don’t want to admit that.
I wonder what sort of studies have been done on this. I found a few with a quick search about admitting being wrong- IT seems to correlate with humility like you would expect. Also admitting fault also sometimes makes people like you more, contrary to the belief that people will think you suck if you admit fault. Though maybe not for politicians, oddly.