Instead of wanting to change the mind of the other entity, how about focusing on coming to a mutual understanding of what is "correct"? That way it shouldn't matter much if said entity is human, LLM or dog. Unless you're just arguing to push your "correct" on other humans, with little care about their "correct".

It feels like you've loaded quite a lot on a way that feels unfair: "pushing" and "little care" etc. I maybe should have used a term like "discuss" target than the more loaded "argue."

Look, I'll give you a loose example: It's not uncommon to see a post making an "error" I know from experience. I might take the time to help someone more quickly learn what I felt I learnt to help me get out of that mistaken line of thought. If it's an LLM why would I care? There's thousands of other people, even other LLMs, that I could be talking to instead.

You've set up a framework here where "mutual understanding" is the end goal but that's just not always what's on the line.