I agree with Anastasia that such feelings usually arise out of pride. We value our own opinions, even exalting them to the level of facts, and when someone dares to express a different opinion, it triggers anger in us that they would contradict what is so very clear to us. I think in that situation, I would pray for God to grant wisdom to myself and the other person. In that way you don't merely make it the other person's problem (which it very well might actually be) but you also ask God to intervene rather than trying to rectify the situation yourself. The demons would be happy to see you get into a heated argument rather than have you seek for God to soften both your hearts.