R. YISHMAEL'S OPINION
Question: According to R. Yishmael, we cannot say that the outer goat atones for a Chet that was not known at the beginning and was known at the end, for he obligates a Korban in such a case;
What does the outer goat atone for?
Answer: It atone for one who did not know at the beginning, nor at the end.
Question: The goats of Rosh Chodesh and the Mo'adim atone for this!
Answer: R. Yishmael holds like R. Meir, who says that the goats of Rosh Chodesh, the Mo'adim and the outer goat all atone for the same thing.
Question: Why was it necessary for the Torah to equate the outer goat to the inner goat?
Answer: This teaches that just like the inner goat atones only for Chata'im of Tum'ah of the Mikdash and Kodshim, also the outer goat.
THE GOATS OFFERED ON MO'ADIM AND ROSH CHODESH
(Mishnah - R. Yehudah): The goats of the Mo'adim and Rosh Chodesh atone for Tum'ah that was never known.
Question (Rav Yehudah): How does R. Yehudah learn this (Rashi; Tosfos - that they atone for Tum'ah of the Mikdash and Kodshim)?
Answer (part 1 - Rav Yehudah): He learns (the goat of Rosh Chodesh) from "u'Se'ir Izim Echad l'Chatas la'Shem." This refers to Chata'im that only Hash-m knows about.
Question: That verse is needed for Reish Lakish's teaching!
(Reish Lakish): In the Chatas of Rosh Chodesh it says "la'Shem" to hint that Hash-m commanded us to bring an atonement for diminishing the moon. (Hash-m needs no atonement. He merely teaches that one who must censure someone should appease them.)
Answer: If it came only for Reish Lakish's teaching, it should have said 'Al Hashem';
"La'Shem" teaches like Rav Yehudah expounded.
Question: Perhaps it teaches only like Rav Yehudah, and not Reish Lakish's teaching!
Answer: If so, it should have said 'Chatas Hashem';
"Chatas La'Shem" teaches both.
Suggestion: The goat of Rosh Chodesh should atone for all Chata'im (that only Hash-m knows about)!
Rejection (Beraisa - Tana d'Vei R. Yishmael): The goat of Rosh Chodesh comes at fixed times, just like the outer goat (of Yom Kipur);
Just like the outer goat atones only for Tum'ah of the Mikdash and Kodshim, also the goat of Rosh Chodesh.
Question: We have answered only for the goat of Rosh Chodesh;
What is the source that goats of the Mo'adim atone for Tum'ah of the Mikdash and Kodshim, even though these are Chata'im of Kares?
Suggestion: Tana d'Vei R. Yishmael's teaching applies also to them.
Rejection: We cannot learn from the goat of Rosh Chodesh, for the Mo'adim come less regularly;
We cannot learn from the outer goat, for the atonement of Yom Kipur is greater (it is for all Chata'im).
Question: We learned Rosh Chodesh from the outer goat, without objecting that Rosh Chodesh comes more regularly (and therefore, perhaps it atones for more)!
Answer: The Torah explicitly writes that the goat of Rosh Chodesh atones. The outer goat teaches only to limit the atonement of the goat of Rosh Chodesh
Here, we seek a source that the goats of the Mo'adim atone. We cannot learn from something that atones more.
Answer (part 2): We learn like R. Chama b'Rebbi Chanina taught;
(R. Chama b'Rebbi Chanina): It says about the goats of the Mo'adim "u'Se'ir." The extra 'Vov' equates it to the previous matter (the goat of Rosh Chodesh).
Just like the goat of Rosh Chodesh atones (for Tum'ah of the Mikdash and Kodshim) when he did not know at the beginning nor at the end, also the goats of the Mo'adim.
Question: If one has no knowledge of his Chet, but others know and (presumably) will tell him, what is the law?
Does R. Yehudah consider this a Chet that is known at the end, and the outer goat atones for it?
Or, is it considered a Chet known only to Hash-m, and the goats of Rosh Chodesh and the Mo'adim atone for it?
Answer (Beraisa - R. Yehudah): The goats of Rosh Chodesh and the Mo'adim atone for a Chet that is not known at the beginning nor at the end, or that others know about and will tell him.
R. SHIMON'S OPINION
(Mishnah - R. Shimon): The goats of the Mo'adim atone for Tum'ah (of the Mikdash and Kodshim) that was never known, but those of Rosh Chodesh do not. (The goats of Rosh Chodesh atone for a Tahor person who ate Tamei Kodshim.)
(R. Elazar): R. Shimon learns from a Gezeirah Shavah "Avon-Avon";
It says about the goat of Rosh Chodesh (when the Mishkan was inaugurated) "Laseis Es Avon ha'Edah", and regarding the Tzitz (the plate on the Kohen Gadol's forehead) it says "Avon"
The Tzitz makes acceptable a Korban whose meat (regarding an Olah, in which the meat is offered on the Altar) or blood or Chelev became Tamei. Similarly, the goat of Rosh Chodesh atones for (one who ate) Tamei Kodesh meat.
Question: The Tzitz makes acceptable Tamei Kodshim brought on the Altar. We should learn that the goat of Rosh Chodesh does the same (R. Shmuel - that it atones for one who brought Tamei Kodshim on the Altar)!
Answer: It says about the goat "Avon ha'Edah" (a sin that only applies to people (R. Shmuel - to Yisraelim)).
Suggestion: Since we learn each from the other through a Gezeirah Shavah, we should say that the goat effects its atonement, and also makes acceptable like the Tzitz!
(Normally, there is no need for something else to make the Korban acceptable, but) this would makes a difference if the Tzitz was broken!
Rejection #1: "Avon (singular)" - the goat only bears one sin, and not two.
Suggestion: We should say that the Tzitz makes acceptable, and also atones like the goat of Rosh Chodesh!
This would give immediate atonement for a Tahor person who ate Tamei meat!
Rejection #1: It says about the goat "Osah (it)" - only the goat bears this sin.
Rejection #2 (to both suggestions - Rav Ashi): It says about the goat "Avon ha'Edah", but not the sin of Kodshim (that were offered in Tum'ah);
It says about the Tzitz "Avon ha'Kodshim", but not the sin of Yisraelim.