What is the significance of harvesting in Taharah?

Rashi: One must harvest grapes in Tahor Kelim, for the juice that exudes from the grapes is Machshir (enables the grapes to receive Tum'ah).

Rashi explained that the juice that exudes from the grapes is Machshir. What is the reason? He does not want the juice to exude. It goes to waste!

Etz Yosef: The Gemara says that this is a decree lest one harvest in plastered boxes. Then, the juice that exudes is collected, and he desires it; it is Machshir mid'Oraisa. Hillel did not decree, therefore he asked why we harvest grapes in Taharah.

Why did Shamai say 'if you anger me, I will decree Tum'ah even on harvest of olives!'? Is this a reason to change the law, in order to avenge one who angered him?!

Rav Elyashiv: The Ritva explains, the decree applies only to grapes, but not to olives, for what exudes from olives is not oil. It is a mere secretion. It cannot be Machshir to receive Tum'ah. They did not decree olives due to grapes, for everyone understands the difference. If you will anger me, and persist in your opinion than there is no difference between them, this is a reason to decree olives due to grapes, for people do not know to distinguish them! If we do not decree on olives, the decree on grapes will not last!

Chachmas Mano'ach: If you [mistakenly] equate them, all the more so we must be concerned lest others do so, so we must decree also on olives!

Why was a sword inserted in the Beis Midrash?

Yerushalmi: Six [Talmidei Beis Shamai] ascended, and the rest of them stood against [Talmidei Beis Hillel] with swords and spears.

Chasam Sofer (17a): The six persuaded some of Talmidei Beis Hillel to agree to some of their decrees. Other Talmidei Beis Hillel wanted to leave, to invalidate a vote. Talmidei Beis Shamai stood with swords and spears to ensure that they not leave].

Daf Al ha'Daf citing Igros Moshe (OC 5:20): One may not enter a Beis Midrash with a weapon! For a great need, to clarify the Halachah, it was permitted. However, what would they do with the sword? If one does not want to give his opinion, is he Chayav Misah?! One who refuses to fulfill an Aseh, we lash him until he dies, but we do not strike him with a sword to kill him! Chizkiyah stuck a sword at the entrance of the Beis Midrash, and declared that anyone who will not learn will be stabbed (Sanhedrin 94b). He should have put the sword in the market, to threaten them to come to learn! Chavatzeles ha'Sharon (2:12) heard from the Aruch l'Ner that one cannot force one to come to the Beis Midrash if he does not understand the attribute of Torah. The sword is needed in the Beis Midrash, lest people mix Kodesh and Chulin.

Why did they say 'one may enter, but one may not leave'?

Rashi: They wanted to count, to see who is the majority.

Rav Elyashiv: The Yerushalmi says that Talmidei Shamai could enter, but not leave; Talmidei Hillel could leave, but not enter. Beis Shamai wanted to be the majority. We can explain that Rashi means like this. (NOTE: I see no reason to explain Rashi like this. Rashi says that they wanted to count to determine the majority! - PF) This is an artificial majority! Outside, Beis Hillel are the majority! I answer that before the Bas Kol, it was not clear whether the Halachah follows Beis Hillel or Beis Shamai. Beis Hillel were the majority, but Beis Shamai were sharper. Beis Shamai held that the Halachah does not follow the majority, rather, the sharpest Talmidim. Klal Yisrael did not accept this. Beis Shamai held that since the Halachah follows them due to their sharpness, if they can become the majority (even artificially), they should do so, to convince Yisrael that the Halachah follows Beis Shamai. Really, such a majority has no clout. Beis Hillel accepted Beis Shamai's words, for they saw that their Rebbi was submissive to Shamai. Therefore, also they retracted. Hagahah - we say that Hillel and Shamai decreed, but it was not accepted! The Gemara is not in order. The episode in which a sword was inserted was later. Perush ha'Mishnayos says that all Chachamim proper for Hora'ah were there, and the majority was like Beis Shamai, for many of Beis Hillel agreed to Beis Shamai's opinion. They forbade people to leave, so the majority would remain.

Why was the day so harsh for Yisrael?

Rashi: Hillel was the Nasi, and he was very humble.

Ha'Boneh: Feuding is harsh in Yisrael. Even when people served idolatry, when there is no dissension between them, punishment do not come upon them. Even though this argument was l'Shem Shamayim, and Hillel was the humblest person, and he sat like one of the Talmidim, since Shamai asserted himself greatly, and a sword was inserted in the Beis Midrash, it was as harsh for Yisrael as the day that the Egel was made, and Yisraelim served idolatry and were punished.

What is the comparison to the day that the Egel was made?

Chasam Sofer: The Nasi (Hillel) was very modest, Shamai did not defer to him, just like Benei Yisrael did not defer to Aharon on the day the Egel was made.

Rav Elyashiv: Aharon did not agree with those who wanted to make the Egel, but he did not oppose them, for he knew that they will not heed him. Also here, Hillel did not agree, but he did not oppose them, for he knew that they would not accept his opinion.

Rav Elyashiv (first edition): Just like had Aharon been stronger, there would not have been an Egel, also here Hillel was submissive, and did not oppose them more forcefully.

Why does it say that Hillel and Shamai decreed, but it was not accepted, and later, their Talmidim decreed, and it was accepted?

Rav Elyashiv: This answers a question. Here, we find that Hillel and Shamai argued about whether or not one must harvest grapes in Taharah. Above, we said that they argued about only three laws, and this was not one of them! We answer that Hillel accepted Shamai's opinion. If so, why is this among the 18 decrees, which were later? We answer that Hillel and Shamai decreed, but it was not accepted. Later, their Talmidim decreed, and it was accepted.