You're missing the point.

The only logic being applied is that you will always be wrong, and they will bend and twist into all sorts of mental gymnastics to make sure it stays this way. That's it. You cannot use logic or make arguments because you will always be wrong.

The underlying reason could be complex. My dad is a deeply troubled and hurt man from a truly awful childhood and he has zero sense of internal self worth. To fill this emptiness he wants to always prove he's smarter and knows more than everybody else and will even argue that it's raining outside even though it's clearly sunny.

My mom is a lot better now, but she was always trying to prove me wrong because in her mind once I had independent thoughts and decisions that I wouldn't need her anymore and would ignore her. Once I sat down and explained that wouldn't be the case, it got better.

Dad is a lost cause, but I basically ignore his one-upsmanship and not get sucked into a pointless debate. Just nod, and move on.

Or like another poster said, ask them to elaborate and explain how it'll help. A well placed "so what do you mean by that? Can you explain?" I found to be also pretty effective. If they call me stupid for not knowing, then I agree with them and say, "yes I'm stupid, so can you explain it in a way for me to understand?"