People people... it is possible to be right AND polite at the same time.
You know that game we play in the beach, with two rackets and a rubber ball? The aim of that game is putting the ball in your couterpart's reach, thus, we could say it is a cooperative game where everybody wins. Now compare that to pingpong, for instance. Basically the same game: two rackets and a ball, but the aim is to defeat the opponent, putting the ball where he cannot reach it. Other than that, both games are pratically the same.
A conversation can be either kind of game. Depends on what you're aiming for. Is it to acheive enlightment for both participants, or to destroy the adversary?