So how does one do the more intelligent and diligent route?

Aye, that's the rub.

Firstly, you "just say no". Argument is for idiots, and exhibitionist argument (aka debate) is for groups of idiots. Refuse to engage in any such idiocy, and encourage others to do the same.

Engage only in earnest discussion [rational discourse] and (ideally) objective study.

Sadly, we cannot (and should not) make the decision to do that for anyone else we are speaking with. We can lead them to water, but we cannot make them drink.

Argument seeks to manipulate (aka convince) others into adopting your position. Discussion seeks to exchange your ideas/position with others - ideally who have differing views (because it is both boring, and generally a waste of time to preach to the choir / live in an echo chamber).

Disagreement is not debate/argument; it's what it devolves into when we aren't careful (and often when we allow emotion to get the better of us - including, but not limited to, the pride of "being right" and "proving them wrong") We must be curious, and seek to explore and evaluate other ideas (especially ones that conflict with our own) as objectively as possible through rigorous/diligent study.