Sounds like you just don't want your authority to be challenged.

If you're wrong and a student points that out, own it. Instead you expect them to question their own knowledge while submitting to your authority for confirmation or denial. But if the student already knows, they don't need your confirmation. They need you to admit that you were incorrect, and move forward with the correct information. Otherwise you're just demonstrating that you're an authority that cannot be trusted to be fair.

Authority that cannot be challenged is authority that cannot be respected. Authority must continually earn the respect of its constituents, or it will lose its power over them.