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We learned in the Daf (Nazir 49b also Keddushin 52b) that Rav Yehuda instructed his Talmidim not to accept into his Yeshiva any Talmid of Rav Meir because they just ask questions to annoy and confuse (vexatious) and not really for the sake of understanding the Torah.
How in the world did Rav Meir's Yeshiva get such an ugly reputation? Talmidim like the great Sumchas (סומכוס founder of the famous klal 'ממון המוטל בספק חולקין') emerged from that Yeshiva, see Gemara there and Eiruvin 13b!!!
In this shuir by R Hartman he quotes Bircas Aharon that (to my understanding) R' Meir hold we do consider the minority, which he extends to considering the arguments of the minority opinion. R Meir's talmidim would then feel that even when their opinion was outvoted and should be irrelevant to the discussion, that they can still bring in their arguments and opinions. These arguments to everyone else were irrelevant because they were predicated on an overruled opinion.
Great question @shayachagigah!
I think the answer is actually in the Gemera in Eruvin 13b that you quoted.
The Gemera says (taken from Sefaria):
אָמַר רַבִּי אַחָא בַּר חֲנִינָא: גָּלוּי וְיָדוּעַ לִפְנֵי מִי שֶׁאָמַר וְהָיָה הָעוֹלָם שֶׁאֵין בְּדוֹרוֹ שֶׁל רַבִּי מֵאִיר כְּמוֹתוֹ, וּמִפְּנֵי מָה לֹא קָבְעוּ הֲלָכָה כְּמוֹתוֹ? שֶׁלֹּא יָכְלוּ חֲבֵירָיו לַעֲמוֹד עַל סוֹף דַּעְתּוֹ. שֶׁהוּא אוֹמֵר עַל טָמֵא טָהוֹר וּמַרְאֶה לוֹ פָּנִים, עַל טָהוֹר טָמֵא וּמַרְאֶה לוֹ פָּנִים.
"On the topic of Rabbi Meir and his Torah study, the Gemara cites an additional statement. Rabbi Aḥa bar Ḥanina said: It is revealed and known before the One Who spoke and the world came into being that in the generation of Rabbi Meir there was no one of the Sages who is his equal. Why then didn’t the Sages establish the halakha in accordance with his opinion? It is because his colleagues were unable to ascertain the profundity of his opinion. He was so brilliant that he could present a cogent argument for any position, even if it was not consistent with the prevalent halakha. As he would state with regard to a ritually impure item that it is pure, and display justification for that ruling, and likewise he would state with regard to a ritually pure item that it is impure, and display justification for that ruling. The Sages were unable to distinguish between the statements that were halakha and those that were not."
The Ben Yehoyada says over there: ונראה לי בס"ד כי הוא היה עושה חריפות זו לטהר הטמא ויראה לו פנים כדי לחדד התלמידים ולראות אם ירגישו לדחות את דברים אלו בטענה של חריפות וכו
"That he would do this חריפות (sharpness), meaning that he would be sharp like that to pure the impure and it seemed to him to do this to sharpen the talmidim, to see if they can reject his words with other objections, etc."
לפע"ד I believe that this was the reason Rebbi Meir got so a bad reputation for his Yeshiva. He taught his students in a way that is not meant to pasken halacha but to sharpen their minds. This seemed like a different approach for everyone at that time, and Rav Yehudah didn't want that way of learning in his Yeshiva.
Maybe we can also add the Gemera in Chagigah 15a that Rebbi Meir still followed Elisha ben Avuyah (Acher), his Rebbi, even though he went off the derech. So maybe that mindset also influenced Rebbi Meirs students thus causing a bad reputation for his Yeshiva.
