As you wrote, "Rebbi Eliezer did not appreciate a question that Rebbi Akiva asked him about slaughtering, and he said, "Just as you asked this question regarding slaughtering with a knife, so you will die by the knife.""
I find this very disturbing. In Pirkei Ovos, 2:8 and 2:9, it states that Rebbi Eliezer was a super great scholar who taught that ayin tovah was the best midah, whereas in today's daf, Rebbi Eliezer had an ayin ra, he did not judge Rebbi Akiva lekaf zchus (who as the Gemora explains was simply trying to avoid hurting Rebbi Eliezer's feelings), and he violated, per the Chinuch, Mitzva 231 - an issur d'Oraysa not to curse a fellow Jew, and especially not someone like Rebbi Akiva. And especially not one's student - is this how one teaches Torah to one's students? It seems from this story that learning great amounts of Torah will not prevent one from being a nasty, vindictive person. (This was actually taught by Reb Yisroel Salanter, but he thought it was not true in earlier generations...)
More amazing, nothing happened to Rebbi Eliezer. Rebbi Akiva did indeed die a gruesome death, and one would have expected the reverse. And one would have expected Rebbi Eliezer to go down in Jewish history as someone to be despised, rather than be praised, as he was in Pirkei Ovos.
Perhaps I am misunderstanding the entire story, I would appreciate any clarification if there is one. I am aware that during the time of the Tannaim and Amoraim, there was great concern for kovod haTorah, and for certain infractions, a Tanna looked at someone and he became a pile of bones - but the story of this daf is totally different - there is a serious halachic discussion going on and Rebbi Akiva is trying to avoid embarrassing Rebbi Eliezer who forgot his teaching (note that he is praised in Pirkei Ovos for not forgetting things...). Many thanks.
Avrohom Meyer Kohn, Los Angeles USA
Rav Chaim Shmuelevitz zt'l, in Sichos Musar (5733, chapter 13), gives an important explanation of this very surprising and difficult Gemara to understand.
1. The first thing we should realize is that Rebbi Akiva was a student of Rebbi Eliezer. The relationship between the Rav and the Talmid is an extremely important one and we can get an idea of this from the fact that the Gemara in Eruvin (63a) tells us that a Talmid who issues a Halachic ruling in the presence of his Rebbe is liable to the death penalty. Rav Shmuelevitz writes (page 45, DH veha'Nir'eh) that the reason why insulting the Rav is such a severe transgression is not because of Kavod ha'Rav as such, but rather because it causes the influence of the Rav in Klal Yisrael to be weakened when Jews are not sufficiently careful about the honor of their Sages and elders. This behavior is tantamount to Klal Yisrael not possessing Chachamim at all. He cites (page 46, DH v'Hu) the Midrash Rabah (Vayikra 11:8) which quotes Rebbi Akiva himself as saying that Klal Yisrael can be compared to a bird. Just as a bird cannot fly without wings, Yisrael cannot do anything without their elders.
2. We can also see the greatness both of Rebbi Eliezer and of Rebbi Akiva from the Gemara in Sanhedrin (68a) which relates the levels of the Torah that Rebbi Eliezer taught to Rebbi Akiva before Rebbi Eliezer died. The Gemara also tells us how Rebbi Akiva could have attained an even greater rank if he would have been an even more devoted disciple of Rebbi Eliezer.
3. Rav Shmuelevitz writes that if the student does not have the correct respect for his teacher, this puts the entire existence of the Jewish people into danger because the tradition of passing the Torah from generation to generation is threatened. Even though the Gemara in Shabbos (149b) tells us that if someone causes his fellow man to be punished, he himself will not be permitted to enter the Mechitzah of Hash-m as a result of what he brought upon his colleague, it is probable that this did not apply to Rebbi Eliezer in our Gemara because Rebbi Eliezer had no personal motives for what he said to Rebbi Akiva, but rather he had to say this in order to guard the honor of the Rav which is essential for the continuation of Klal Yisrael.
4. Hence, even though Rebbi Akiva was indeed trying not to hurt Rebbi Eliezer's feelings, on the other hand Rashi (69a, DH b'Shechitah) explains that Rebbi Akiva knew that the Kal va'Chomer which he taught was incorrect and this represented ridicule of Rebbi Eliezer for someone on such a high level as Rebbi Akiva, which meant that an extremely high standard of respect was expected from him.
5. In short, there was nothing personal in the way Rebbi Eliezer behaved but since he was such a great teacher, and since Rebbi Akiva was such a great Talmid, an incredibly high level of respect was expected from their relationship.
Kesivah v'Chasimah Tovah,
Dovid Bloom