The short-sighted

This may be related to what is written in the Talmud that the law was not terminated by Rabbi Meir because they did not reach the end of his thought. That is, even if they were certain that they did not understand him, they were not afraid to fortify their position.

But there, in my opinion, it's because there is value in autonomous ruling, even if it's not the truth. I've explained this at length in the past.

What is it?
In the case of the Deshmia, I must judge according to my own opinion, which is also wrong, but in the case of the Dema, I should give more room to the fear that I may have missed something and strive more for the truth?
Who is the priestess and who is the innkeeper?

Just to clarify, I didn't mean "should" in any sense of obligation. It's hard for me to think of another word right now in my sins.

Nothing to do with the priesthood and the innkeeper. This is not a question of severity and tone. In the matter of Halacha, one does not seek the objective truth, but the truth in my opinion. In other matters, the goal is to reach the truth. For example, if there is a person who is smart in physics and it is clear to me that he is smarter than me, then even if I think differently from him, I would ‘rule’ like him, because apparently the truth is with him. But in Halacha, I do not conclude with a ”ruler” even though the truth is with him, because in Halacha there is value in acting autonomously even if it is not the truth.

Rabbi Bemcha”t If, according to your words that seek the truth, in my opinion, why would Rabban Gamliel harass Rabbi Yehoshua who disagreed with him and demanded that he come to him on his Yom Kippur and all the other harassment? Didn't he know that there is value in autonomous ruling? And why did Rabbi Yehoshua agree to violate Yom Kippur and not insist on it? Would you agree?
If you say that I am Rabban Gamliel who was the president of the Sanhedrin and all the sages are obligated to him, then why did the sages remove him from the presidency due to his coercion of Rabbi Yehoshua?

There we are talking about a Sanhedrin that has formal authority. Secondly, the calendar is under the mandatory authority of the president of the Sanhedrin and is not given to anyone. You are even joking…
Why was he deposed? Because he used his authority too wildly, and not only in this case.

And by the way, your message contains an internal contradiction. You bring evidence from a man who apparently determines the truth, but immediately afterwards you wonder why he was deposed, and bring counter-evidence from that. He was deposed precisely because he followed the truth and did not listen to autonomy.