The concept of a Universal Turing Machine (UTM) suggests that, given enough time and memory, it can compute anything that is computable. By extension, if human cognition is computable, a sufficiently advanced computational system could, in theory, model and explain it.
This doesn't necessarily mean we'll easily achieve this understanding, as the computation required might be extremely complex and time-consuming. But it does suggest that the explanation of cognition isn't fundamentally beyond reach, even if we're using the system to explain itself.
(Meaning that we may not be smart enough to be able to explain why and how we are smart enough to explain our cognition, if we can explain it at all)