Being wrong is okay. It is how we learn. We were once wrong countless times as infants as we learned to navigate our environment. We were wrong in school, when we were corrected by our instructors. We are even likely wrong about some things right now, but aren't aware.
It isn't being wrong that is problematic. It is being wrong and not learning how to become less wrong and more correct. Reason will lead us more and more toward truth as long as we are willing to follow its light.