Changing your mind when you learn something isn’t weak. Refusing to is just pride with a loud voice.

Updating a view when new information arrives is the entire mechanism of getting things right. It gets read as inconsistency because people treat positions like property, as though giving one up were a loss rather than a trade. The refusal is usually not about the evidence at all. It is about how it would look to move.

Say the change out loud next time it happens, with the reason attached: what you used to think and what changed it. Doing it in public breaks the habit, because nobody thinks less of you and several people trust you more.