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In addition to what I wrote in the other comment, a critical skill is to imagine the possibility that someone close to you may be manipulating you.
I am not saying that you must suspect all people all the time. But when strange things happen and you notice that you are confused, you should assign a nonzero value to this hypothesis. You should alieve that this is possible.
If I may use the fictional evidence here, the important thing for Rational!Harry is to realize that someone close to him may be Voldemort. Then it becomes a question of paying attention, good bookkeeping, gathering information, and perhaps making a clever experiment.
As long as Harry alieves that Voldemort is far away, he is likely to see all people around him as either NPCs or his party members. He doesn't expect strategic activity from the NPCs, and he believes that his party members share the same values even if they have a few wrong beliefs which make cooperation difficult. (For example, he is frustrated that Minerva doesn't trust him more, or that Dumbledore is okay with the idea of death, but he wouldn't expect either of them trying to hurt him. And the list of nice people includes also Quirrell, which is the most awesome of them all.) He alieves that he lives in a relatively safe bubble, that Voldemort is somewhere outside of the bubble, and that if Voldemort tried to enter the bubble, it would be an obviously extraordinary event that he would notice. (Note: This is no longer true in the recent chapters.)
Harry also just doesn't want to believe that Quirrell might be very bad news. (Does he consider the possibility that Quirrell is inimical, but not Voldemort?) Harry is very attached to the only person who can understand him reliably.