I'm going to be kind. (I know, weird, right?)
There is NOTHING wrong with being incorrect. No one is correct all the time.
There is nothing wrong with being careless with being incorrect. We ALL do it, some more than others, but still.
There IS something wrong with not taking responsibility and owning your mistakes. There IS something wrong with not working to be less careless.
There is NO growth or learning when one will not admit they've made a mistake and had a misconception.
If you ignore your mistake and pivot or move the goal post, you lose ALL credibility among anyone with higher than a room temp IQ.
That shame one feels when they're wrong is there for a reason: Growth. To deny and cover up that shame is to NEVER grow.