So the thing is nobody is rational. "Rational" people are at best people who have as psrt of their self image that they are rational, so feel discomfort when confronted with rational arguments that disagree with their behaviours or beliefs.
My understanding of the neuro- and cognitive sciences say this is not quite right. It'd be more accurate to say that people can be rational, but they have to work at it and don't always manage it.
Thing is, deciding what to do "rationally" is insanely hard. Nobody is actually smart enough to do it.
Sure we are. The issue isn't one of being "smart enough". It is about being aware what it going on inside your head, and purposefully setting up patterns to avoid traps. You might consider that, in fact, each of us is of two minds. They speak with the same voice, though, so it can be hard to distinguish them if you aren't careful.
The human brain has a set of structures collectively called the "limbic system". It is responsible for regulating your endocrine system, processing your response to emotional stimuli, and reinforcing behavior. For our purposes, you may consider this the "Oh sh*t, jaguar!" portion of your brain. It isn't precisely illogical, so much as it is based on getting you a fast response based on only small bits of information. When there is, in fact, a jaguar in the tall grass, you want the limbic system, as it gets you the fear response you need to rev up your adrenaline and get your feet moving. When there may be a jaguar, the cost of being wrong is small, compared to the value of being right, so the limbic response is useful and appropriate.
You also have structures in your brain that can process cold, clear logic very well. But they are glacially slow compared to the limbic system. By the time you have processed a rational response, the limbic system has already gotten its answer out there, and you're already acting on it.
Also relevant for our discussion - the limbic system does not differentiate between physical and social threats. Someone coming at you with a club is not all that different from a person about to cause you great loss of face, from the limbic standpoint.
Our collective problem being that there are very few jaguars any more. For modern life, we really want the reasoned response that is so often drowned out or colored by the limbic response. And, we can get it, but it takes practice to filter out the nonsense, and anyone can occasionally fail.