There is more to the human brain than just classical computation. Humans can easily understand concepts and deal with ideas that are beyond the limits of any classical computer. For example, the concept of infinity can be generally understood by an intelligent 8 year old. Consider counting an infinite set of real numbers, starting from 1 and counting upwards by 1, FOREVER! There is no computer (or person) capable of actually performing such a computation. Yet, using simple language, we’ve just formalized that concept and can easily represent it as: S = {1, 2, 3, 4, . . . }.
Of course you can program this compression into a classical computer, but the computer doesn’t have understanding or intuition around the implications of such an idea.
Many people in the artificial intelligence space think that applying increasing levels of compute will produce a version of consciousness in the system, but this is a mistake. It will produce more intelligence, but that intelligence will always need a conscious manager to direct and correct its course.
I could be wrong.