Things are rarely formal logic with inerrant premises.But once their error has been exposed, and they stubbornly cling to it anyway, THAT'S when the contempt sets in. Once they have been presented with, "All men are mortal, and Socrates is a man, therefore, Socrates is mortal," they're not allowed to continue to insist that Socrates is immortal without drawing their fair due of ridicule.
Many things presented as fact are really just opinion.
And reasoning is fuzzy.
I don't think that "reason" takes offense.But again, it's not me that is offended, it is reason that is offended. As an ally of reason, I cannot abide those who offend it. I don't take it as a personal offense, I take it as an offense to humanity, and our responsibility as rational beings to hold rational beliefs.