1) BURNING "TAMEI" MEAT INSIDE THE AZARAH
QUESTION: Beis Hillel rules that the meat of Kodshei Kodashim that became Tamei must be burned outside the Azarah. If, however, it became Tamei with Velad ha'Tum'ah while it was inside the Azarah, it may be burned inside the Azarah. The Gemara quotes Bar Kapara who explains that this Velad ha'Tum'ah refers to Tum'ah d'Rabanan.
The Gemara challenges Bar Kapara's opinion. According to Bar Kapara's opinion, Beis Hillel should not differentiate between an object that became Tamei inside the Azarah and one that became Tamei outside the Azarah. If Velad ha'Tum'ah is a Tum'ah d'Rabanan, then even if the object became Tamei with Velad ha'Tum'ah outside the Azarah, one should be permitted to bring it back into the Azarah (and burn it there). The Gemara answers that, according to Bar Kapara, Beis Hillel follows the opinion of Rebbi Shimon who says that the food of a Metzora must be kept out of the Beis ha'Mikdash (and out of all three Machanos). Similarly, meat that is Tamei must be sent out of the Beis ha'Mikdash.
If Beis Hillel follows the opinion of Rebbi Shimon, then even if the meat became Tamei with Velad ha'Tum'ah inside the Azarah, one should be required to send it out of the Azarah. Why is he permitted to burn it inside the Azarah?
(a) RABEINU MESHULAM and the VILNA GA'ON (as explained by the TIKLIN CHADTIN) explain that Rebbi Shimon does not mean that the food of a Metzora must be sent out of the Beis ha'Mikdash. Rather, he means that if it is already out, then it must be kept out. If, however, it is in the Azarah, it does not have to be removed. That is why Beis Hillel differentiates between meat that became Tamei inside the Azarah and meat that became Tamei outside the Azarah, according to Bar Kapara who says that it became Tamei with a Velad ha'Tum'ah.
This implies that if the meat became Tamei with an Av ha'Tum'ah, it must be sent out of the Azarah. If the food of a Metzora may remain in the Azarah, why must Tamei meat be removed from the Azarah? Apparently, the requirement to send it out of the Azarah is only a stringency enacted by the Rabanan due to the severity of the Tum'ah, a Tum'ah d'Oraisa.
(b) RABEINU SHLOMO SIRILIYO explains that Rebbi Shimon stated his ruling only with regard to the food of a Metzora. Rebbi Shimon derives from the verse, "His dwelling place shall be outside of the Machaneh" (Vayikra 13:46), that not only must the Metzora himself stay outside of the Machaneh, but the Metzora's food also must remain outside of the Machaneh. A person's food is called his "dwelling place" (as the Gemara says in Eruvin 73a).
If the meat becomes Tamei with Velad ha'Tum'ah while it is outside the Azarah, it must remain outside the Azarah because of this law of the food of a Metzora. Even though the Gemara's case here discusses meat of Kodshim (and not food of a Metzora), the Rabanan decreed that the meat not be brought into the Azarah lest people confuse it with the food of a Metzora (both are burned due to their Tum'ah) and bring the food of a Metzora into the Azarah. However, when the meat becomes Tamei while inside the Azarah, no one will think that is the food of a Metzora, because there is no way that a Metzora could have brought his food into Yerushalayim.