This already falls apart though. There are while categories of things which I find "incorrect" and would take up as an argument with a fellow human. But trying to change the mind of an LLM just feels like a waste of my time.
It often is with humans as well.
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.
Arguing for the sake of convincing onlookers reading the conversation is more likely to be effective, and in that case it doesn't matter if the other person is an LLM.