At the beginning of his Rhetoric, Aristotle discusses the three ways we persuade an audience: from logic, emotion, or character.
Argument and emotion seem entwined. Why argue unless we are emotionally motivated? I suppose there is the hopelessly disingenuous who argue for argument's sake, as Hume would have it, but there cannot be that many.
As for character, take the hypocrite. We stop listening to him no matter what he says. If your opponent is a hypocrite, show him to be that. You have a chance at winning the argument even if he does have the better case.