This is related to cognitive dissonance. If you think you're rational because everything in your head makes sense to you, and someone comes along and says you're wrong, that's going to cause dissonance.
And if you're not very skilled with handling internal dissonance because you've never learned how (therapy, critical thinking skills, negotiation, communication skills, extrospection), then that might show up as combative arguing or even anger.
Especially if ego is challenged by the conflicting cognition.
One way to describe ego is, it's who you think you are.
So if I think I'm rational, and someone tells me I'm not, and I have never learned the skills to handle this feeling, then I might see it as a personal affront to the ego belief in "I am a rational person."
And that will amplify dissonance exponentially.
The more attached to the ego belief one is, the more powerful the dissonance reaction from having it challenged. The mind experiences it as a threat to existence itself.