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It’s true that the less precise answer makes it harder to be wrong, but you want to find out when you have the wrong answer if you are going to get better at math.
Part of why it’s easier to see other people more objectively than you can see yourself is that you are motivated to protect your beliefs when it comes to reasoning about your own situation. Your beliefs form the fabric of your identity. Discovering that you’re wrong about something, questioning your beliefs, or admitting that some bad outcome was because of a bad decision you made and not just bad luck—these all have the potential to tear that fabric.
We are all motivated to keep that fabric intact. When it comes to your own reasoning, your beliefs end up in the driver’s seat steering you toward a narrative that protects your identity and self-narrative.
Smart people are also better at constructing convincing arguments that support their views and reinforce the things they believe to be true. Smart people are better at spinning narratives that convince other people that they are right, not in the service of misleading those people but in the service of keeping the fabric of their own identity from tearing.
The combination of motivated reasoning, the propensity to mislead yourself, and an overconfidence in intuition makes smart people less likely to seek feedback. When they do seek feedback, their ability to spin a persuasive narrative makes other people less likely to challenge them.