In an fictional argument between a purely rational ans a purely emotional person the first person who considers themselfs rational, might outlook the meaning of the argument for the second person which is having an emotional attachment not to the argument itself but to what it means for them on a emotional level.
The first person might be seen arrogant or cold because they dont understand that being right for the emotional person is actually an emotive state which the person wants to fulfill.
The first person is usually lacking in such emotional powerful reaction regarding the arguing and maybe even in day to day emotional life.
But the second dosent.
So when this two persons meet its an incredible misunderstanding.
Because the first dosent understand the emotional reaction of the second and they might not give up especially if they have good facts which back them.
But for the second person, that feeling of being right is what they’re looking because of they’re nature, as purely emotional.
They don’t usually understand how can the first person be so insensitive and cold because they’re clearly dont care emotional about the argument so they fail to grasp the rational side of the others person and they might think the rational one is doing it in spite.
And the rational person might think the emotional one dosent understand or just wants to argue or be right in a bad manner. But they also fail to grasp the meaning of that emotional state because they dont have that emotional state.
As a simple explanation a purely emotional person sees arguing as a play or as an activity involving the emotional side. While a rational one seeks the truth in the argument but to satisfy his mental state.
So bouth wants satisfaction, one emotional, one mental.