> The point of an argument is to convince the other person of something. If what you're doing is not working, then do something else.

That's not the point of most arguments. Most arguments have an audience, and often that audience is also involved in making choices.

If neither your opponent nor your audience is swayed, yeah, you could just be entrenching everyone in an oppositional attitude.

That being said, discussions are typically better than arguments when that is an option.