That’s certainly admirable if true, but you can’t force anyone to accept that your own notions of what constitutes a compelling argument are the right way to decide what to think. Arguments almost never resolve themselves like a math equation, because there are always things people cannot understand about each other and their perspectives, and there are always things you do not understand about the world.
You mention religious zealotry in another comment. Have you ever had a long argument about spirituality with a very religious person trying to convert you, who has a sincere and elaborate concept of why their religious beliefs are undeniable? Such people think that given the essential truth of their beliefs, if only you could be made to see that truth you couldn’t help but be persuaded, and that it would be useful and just to continue trying to persuade you indefinitely. And the logic is coming from a place other than an orientation around evidence and discovering the world on its own terms without assumptions that a scientific rationalist might have, but you can still see somewhat that in their minds it all fits together given their worldview. It isn’t some intellectual decay. And neither is it the case that you aren’t converting to their religion because you have made a mistake or have some failure of spirit, but they can’t or won’t see that. And at some point you just have to accept that they’re never going to see it, and say “I just disagree” even though you’ve heard and considered what they have said, even though you may not entirely comprehend whatever spiritual feeling they are trying to convey to you. That is not a failed argument, it’s a fine way for a conversation to go.
What makes a good argument is that, in the end, everyone understands each other and their thoughts and feelings a little better. Approaching it with the attitude of a conqueror isn’t the best for that I think, it’s just obnoxious and makes people want to dig in their heels about whatever the topic is.