"Rationality" is at best a filter of rule constraints applied to small part of solutions that reach consciousness in any solution-seeking process. As we know eg. from Lakoff and Johnson ('metaphors we live by' etc.) most of reasoning is actually done using our sensory faculties, mostly spatial, which barely guarantee any kind of correctness.
If you try to be rational and cling to concepts while trying to figure out an answer to difficult problem, you obstruct the process rather than help it. Hence the popular advice to 'forget about the problem' so that the mind can figure it out by itself. How on earth is it rational? Rationality is only applied when checking a solution, like checking a proof, which - as we know - is orders of magnitude less computationally complex than finding a proof.
The mind is all about 'what works' not 'what's correct', rationality is pretty modern invention and to honestly think that we're primarily rational is a delusion. Tversky and Kahneman's work is another obvious counterexample.