“It could turn out that the human mind is constitutionally unable to understand itself.” 
Take this case. If mind-brains are "formal systems", it may be the case that they couldn't have complete knowledge of themselves. John Heil writes:
“Gödel showed us that formal systems rich enough to generate the truths of elementary arithmetic were, if consistent, in principle incomplete. (A system is incomplete if there are truths expressible in and implied by the system that cannot be proven true in the system.) The incompleteness of mathematics reflects an established fact about the make-up of formal systems generally. Now, imagine that we finite human beings are, as we surely are, constitutionally limited as to the kinds of thought we could entertain. Imagine, further, that our cognitive limitations were such that we could not so much as entertain the deep truth about our own minds.” 
It is indeed quite wrong to simply assume that the "deep truth" (or truths) of mind will some day be available to us (as many scientists may imagine). Heil writes:
“Indeed, we should be hard put to establish in advance that the deep truth about anything at all – including the material world – is cognitively available to us. To think that it must be is to exhibit an unwarranted degree of confidence in our finite capacities, what the ancients called hubris.” 
“… we cannot positively prove that we are cut off from a deep understanding of mental phenomena.” 
Heil, John. (2004) Philosophy of Mind: A Guide and Anthology.