An argument is a disagreement among friends, or at least among neighbours, intended to bring both parties closer to the truth about the thing being discussed. This being so, an argument is always a noble exchange between two noble interlocutors with a noble goal in mind. A quarrel, on the other hand, is a disagreement among friends or neighbours which very quickly turns them into enemies. The goal of a quarrel, as distinct from an argument, is not to bring the other to the truth but to beat him into submission. 

An argument is inspired by the charity which a quarrel lacks. It is for this reason that the love of truth which animates a good argument leads to the love of the truth-seeker with whom we are arguing. To put the matter succinctly, caritas leads to claritas, which is another way of saying that love leads to reason.

Joseph Pearce, "Arguing but Never Quarreling"