Why a Machloket ended so badly and unpeacefully?

Question

Back to Tanuro Shel Akhnai (BM 59b). A short recap:

• R' Eliezer and Chachamim are having a Machlokes over a minor matter in ritual impurity, clearly for the sake of Heaven.

• R' Gamliel, the Nassi, instructs R' Yehoshua and Chachamim to stand up blindly against R"E (he accepts the responsibility for the incident a couple of lines below)

• All Facts, including the Heavenly voice, point that R"E is right.

• R"Y still decides to stand up against Heaven and to rule differently. R"E leaves the Beis Midrash.

Up until now, it seems like an everyday argument. But things get completely wrong from this point on:

• Chachamim decide to curse R"E and to boycott him (and all his following Psakim, Rashi). They send R' Akiva to inform R"E of their decision

"His (R"E) eyes shed tears, and as a result the entire world was afflicted: One-third of its olives were afflicted, and one-third of its wheat, and one-third of its barley. And some say that even dough kneaded in a woman’s hands spoiled. The Sages taught: There was great anger on that day, as any place that Rabbi Eliezer fixed his gaze was burned."

"And even Rabban Gamliel, the Nasi of the Sanhedrin at Yavne, the head of the Sages who were responsible for the decision to ostracize Rabbi Eliezer, was coming on a boat at the time, and a large wave swelled over him and threatened to drown him."

• R"E continued to hold grudges at R"G and the first opportunity he had, he ... did something and R"G, his brother-in-law died.

• R"E continued to be totally boycotted for the rest of his life.

What started as a Machlokes Lashem Shamayim, ended pretty badly. It is absolutely clear to me that the Sages could behave differently, appeasing R"E, welcoming him back and ending the incident peacefully and drink Le-Hayim.

How can this be reconciled with the Gemmorah (Brochos 64) we say every day in the final part of the Tefilah:

אמר רבי אלעזר אמר רבי חנינא: תלמידי חכמים מרבים שלום בעולם שנאמר וכל בניך למודי ה׳ ורב שלום בניך

Rabbi Elazar said that Rabbi Ḥanina said: Torah scholars increase peace in the world

??

Answer 1

Rabbi Eliezer refused to accept and teach the decision of the majority of the Sanhedrin. That was a cardinal sin. The object of the decision matters little. Same story with Rabbi Akaviah ben Mahalal'el.

The Rambam codified that principle:

לנטות אחרי רבים אם תהיה מחלוקת בין הסנהדרין בדינין, שנאמר: "אחרי רבים--להטות" (שמות כג,ב).

To give the decision according to the majority, when there is a difference of opinion among the members of the Sanhedrin as to matters of law, as it is said, "To incline after many" (Ex. 23:2).

Rabbenu Bahya [on Numbers 16:22] tells us that that principle was applied in our case:

Rabbi Gamliel who had put Rabbi Eliezer in ban for his publicly disagreeing with the majority decision of the other sages.