Another great post.
Cognition and cogitation are functions of man, not of our brains: This is the thrust of our misconception.
IMO the root of this dualism is not only pervasive in neuroscience, but also in physics, astronomy, and evolutionary biology. In the simplest terms, I believe it is the ultimate reluctance to consider ourselves in position that is not unbiased by our awareness. Even efforts to consider ourselves from a perspective of experimental fact, are usually presented as lessons in humility or exercises in uncommon thinking, rather than a foundation on which to build a consistent model that includes ourselves and everything else.