My opinion is that anger is the manifestation of frustration. Some (or should I say many?) people become frustrated when they are unable to easily persuade someone else to their way of thinking. Such words as argument, quarrel, etc., are used to describe the outward manifestation of such frustration. Usually such things can be eliminated by (a) listening with an open mind to the other side of the discussion or (b) searching more carefully for ways to clearly state your opinion - or more likely a combination of both (a) and (b).