Yes, our reasoning is fallible, I acknowledge this. Though I wouldn’t call an imperfect conclusion, valid reasoning.
Well, “it is not a stretch” is not very convincing! People do believe they are agents, that they are the source of their thoughts. The courts agree, “movement of atoms in my brain made me do it” is not going to fly. Only the materialists think this is a delusion. Imagine that! It reminds me of Hinduism, where an illusion, inside an illusion, is trying to convince me that I myself am an illusion. Why should I believe you, or the Hindu?
As C.S. Lewis points out, “The description we have to give of thought as an evolutionary phenomenon always makes a tacit exception in favour of the thinking which we ourselves perform at that moment. … our present act, claims and must claim, to be an act of insight, a knowledge sufficiently free from non-rational causation to be determined (positively) only by the truth it knows.”