Why did you blush so much?!

I read it, thanks. Bottom line: There is no good solution to this problem. If you explain to yourself what your partner's psychological problem is (locked in, fixed, etc.), it doesn't break the symmetry when he thinks the same thing about you.

Is the fact that he's wrong supposed to impress me? Anyone can make any claim. So what? Why does the claim that there are others who say differently than me prove anything? Then they're wrong. And if they think I'm wrong, that's obvious. It's a logical consequence of their mistake.

Not their claim itself, but their authentic perception that you are wrong and they are right. When I step outside myself and zoom out, I am facing another and I am unable to break the symmetry with arguments that are not subjectively dependent on my personal perception. Peers disagreement is a blunder with no real end in sight, although it of course leads to absurdly skeptical results.

But why do you have to get out of yourself? Is that even possible? You are you and not someone else. Think about the judge who hears the arguments of both sides. They themselves do not know what the truth is, and the parties do. There the judge is really supposed to relate to the situation from the outside because he does not have direct access to the factual truth. But in an argument between the parties, am I supposed to step into my friend's shoes and judge the situation from the outside? If I am right, he is lying or wrong, and that is it.
This reminds me of the question of Maharishi Basan, why is the detainee allowed to keep the money without evidence, since there is doubt about the prohibition of theft. The question is obviously unfounded, since he himself knows that he is right, the doubt lies only with the judges and not with him. Is he supposed to take some objective view and declare that he is in doubt because the judges do not know the truth? Therefore, there it is clear that the question is not difficult, except in the case of Beri and perhaps to exclude, that the detainee himself is really in doubt.

The examples you gave are irrelevant precisely because of the subjective asymmetry in them. The defendant knows what the court does not know. I am talking about my factual argument and my colleague has the same knowledge. I am not telling him anything. He simply concluded differently. I can even explain to myself that he is fixated, has pride that is unwilling to admit a mistake, etc. But if I have a real indication that he also thinks the same way about me in his heart, I have no reason to prefer my opinion over his.

As for whether it is possible: That is a good question. But it is a psychological question, not a philosophical one. I am talking about what is appropriate.

Even in our current debate, I am forced to admit that I have to remain skeptical about the claim that peer disagreement is a problem without a solution, given that you think otherwise.

I will preface this by saying that this was not just a psychological claim but also a substantive one. I cannot leave because I do not need to leave. When I address the question of what my opinion is, it is by definition my own opinion and not the opinion of someone from the UN. Even in the question of whether I am right (the PEER question), the one who decides is me. I claim that the requirement to take an objective view of this particular question is not well defined.
I claim that we do not have the same knowledge. My conscious observation (of ideas) gives me information that I believe he did not reach. He is blind to certain aspects of the ideal world.
Your sly comment at the end is very kind.

“I argue that the requirement to take an objective look at this particular question is not well defined”
Are you arguing that the peer problem doesn't even begin? Were pens broken for nothing?

First of all, there are quite a few pens that get stuck on undefined questions. Unfortunately, too many. Second, absolutely not. The question is good within the framework of my discussion with myself: Should I fear the righteousness of the other? And my answer is that within the framework of my thought, it is not right and not defined to demand going outside, and if we are dealing with my perspective, then it is indeed justified to rely on my own conclusions.