I don't argue if I don't think I have to.
Show, not tell.
If I think I'm right, I won't go out of my way to keep saying it. I'll do something to show that I'm right, or in other words, present irrefutable evidence that the opposite party is clearly wrong.
If I don't think I can prove I'm right, then there's no reason to argue in the first place at all. How can I claim someone is wrong when I can't prove that I'm right?
And this goes both ways. If I have a feeling the opposing party cannot prove their side, then I'll have them show me the evidence. Show me the numbers, the data, the research, whatever it takes. Who's the source? What is the source? When was this information published? If the opposing party is so concerned with proving me wrong, I'll gladly accept "defeat" if they can back themselves up. Otherwise, it's all just fluffy words. If they won't give it up, then they can live in ignorance. It's their loss, not mine. I can go about my day just fine.
No support = nothing proven. All assumptions and/or opinions and therefore neither right nor wrong.
I've gone without any issues professionally and personally by behaving this way for the better part of the last decade.