The error is in overestimating the importance of surface similarity. If I know something, I don’t necessary have an argument that would convince you, and there is no “right to convince” that should change your belief despite the absence of argument. Similarly, there is no right to convince yourself. Just knowing something is not a very strong argument in favor of coming to believe it, of changing the other beliefs about the same fact that assert contradictory things. To change a belief, you need to consider an argument (evidence) about it, not just an assertion of a contradictory belief, even if both happen to be present in the same mind.
The error is in overestimating the importance of surface similarity. If I know something, I don’t necessary have an argument that would convince you, and there is no “right to convince” that should change your belief despite the absence of argument. Similarly, there is no right to convince yourself. Just knowing something is not a very strong argument in favor of coming to believe it, of changing the other beliefs about the same fact that assert contradictory things. To change a belief, you need to consider an argument (evidence) about it, not just an assertion of a contradictory belief, even if both happen to be present in the same mind.