The common motivation, and goal, of arguments is to win the other person over to your point of view. However, this is often done abrasively, which can quickly lead to nowhere as people get defensive and resort to merely defending their positions instead of trying to influence the other person to change theirs.
I think the motivation/goal of an argument should not be to win over the other person, but to lay out your point of view and reasons for said view. If done logically, and respectfully you might just win them over to your side, but only as an added bonus.
Furthermore, one could argue that arguments are simply essential thought experiments which allow us to test, change, or reinforce our beliefs on a variety of topics.