For anosognosia to be a common failure mode, and for the split brain patient's peculiar left side's behaviour, the rationalization got to be a common mode of thought. Perhaps there's a module in the brain that prepares speech but has very little impact on the beliefs and decisions; I ask you why your hand is not scratching your back, and it says, because my back is not itching, and that happens to be correct, but it would say same if the arm was paralysed and back was itching and it wasn't 'told' (by the part doing actual thinking) that arm was paralysed.

When you say you aren't rationalizing, perhaps that module still works by rationalization, it just happens to be quite plausible. Maybe that's how construction of sentences works in the first place when talking about nearly anything.