It's not that hard to accidentally believe a contradiction, since we're not logically omniscient and "consistency checking" is a computationally intractable problem except in simple cases.

I agree with you in theory, but in practice there are plenty of contradictions which are pretty darned obvious. i.e. the limiting factor in human rationality seems to be the human tendency to self-deception and hypocrisy. As opposed to the computational difficulty of finding contradictions.