The mind gives extra weight to whatever confirms what it already believes.

Confirming evidence gets accepted quickly, and contradicting evidence gets examined for flaws. Both feel like ordinary thinking from the inside, since you are indeed being rigorous, just asymmetrically. This is how intelligent people become more confident and less accurate at the same time.

When something confirms what you already thought, give it the same scrutiny you would give the opposite. If it survives, good. Applying equal standards is most of what careful thinking actually consists of.