@MJA,
We perhaps do not have access to it. Perhaps our knowledge is not all encompassing. Perhaps even our ability to express simple ideas is limited. Perhaps language itself is limited.
Consider also that the theory would not be of everything, but rather a theory of human interaction with the environment in which man is placed. The reality we experience is clearly one based on relation,i.e. all experience is based on how we interact with and perceive one thing relative to another. There are no absolutes since we base our definitions, language, ect all on that with which we interact, so is it any surprise that we can generalize back to a single trait or rule? We simply think of all things with respect to each other, so any conception of truth or unity is simply due to human cognition and its limitations. It could very well be the case that we view all things as unified because of our limited perspective. We are, after all, directly related to what we experience, but since this is the case; how could we say that it is not possible that we define what we experience, hence it all relates to us?
I do not think it possible to create a framework of human interaction, as we must turn the lens of rationality upon ourselves to see it, but the lens, like the eye, cannot see itself. Hence, there shall be problems with completeness, because of the inherent relativity in our interactions, and there will be problems with certainty, as we can fill ourselves with doubt.
Many look to Goedel's incompleteness theorems as evidence that there cannot be a theory of everything. This may or not be the case, though it is certainly reasonable to claim it so. That something can be viewed in two ways and appear completely different in each, is a simple truth, yet it may be the key to why we cannot have a theory of everything. Though, I would be suspicious of any claims of limitations to that effect.
I would be suspicious still, of any assertion that we cannot know everything, for it draws a limit to that which is drawing the limit, i.e. we will have a human who knows what is not possible to know, for to know that something is not possible to know, it seems that one should have to know that such a thing exists, and to know it exists, they must have experienced it in some way. Though to even assert this we may tread in dangerous and uncertain waters.