QUESTION: The Gemara says that when the Kohen Gadol wears the Tzitz upon his forehead, it appeases (Meratzeh) for a certain Pesul that would normally invalidate a Korban from being offered. As long as the Kohen Gadol wears the Tzitz, that Pesul does not invalidate the Korban.
The Beraisa asks for what Pesul the Tzitz appeases. It cannot be the Pesul caused by a Kohen who thinks about eating or offering the Korban in an improper time or improper place ("Chutz l'Zemano" or "Chutz l'Mekomo"), because the Torah says that a Korban is never accepted with such a Pesul; even the Tzitz cannot permit it. The Beraisa explains that it must be that that Tzitz is Meratzeh for a Korban that became Pasul as a result of becoming Tamei. The Beraisa adds that it makes sense that the Tzitz should be able to be Meratzeh for a Korban which became Tamei, because there are other cases in which a Korban that is Tamei is acceptable, such as a public Korban, which is not invalidated by Tum'ah, because of the principle of "Tum'ah Hutrah b'Tzibur."
Why does the Beraisa find it necessary to give an additional reason to prove that the Tzitz compensates for the Pesul of Tum'ah? The Beraisa here (and the Gemara in more detail in Menachos 25b) already proves by the process of elimination that the verse teaches that the Tzitz compensates for the Pesul of Tum'ah. Why, then, is it necessary for the Beraisa to prove further that Tum'ah is not an absolute Pesul from the principle of "Tum'ah Hutrah b'Tzibur"?
ANSWER: RABEINU TAM (cited by Tosfos here and in Yoma 7a) explains that the verse that teaches that the Tzitz is Meratzeh says that through the Tzitz, the item that is Pasul will be "l'Ratzon Lifnei Hash-m," acceptable unto Hash-m. These words imply that the Korban will become acceptable to Hash-m just as elsewhere the same Pesul can become acceptable. Accordingly, the Pesul for which the Tzitz is Meratzeh must be one which is "Hutrah mi'Klalo" -- a Pesul that does not disqualify the Korban under certain circumstances even without the Tzitz. For this reason, the Beraisa adds that the Pesul of Tum'ah indeed is permitted elsewhere ("b'Tzibur"); this shows that it fits the description of the verse.
However, if this is true, then why does the Gemara even consider that the Pesul for which the Tzitz is Meratzeh is "Chutz l'Zemano" or "Chutz l'Mekomo"? Those Pesulim are never permitted under any circumstances.
1. TOSFOS (DH Ha Eino) says that there is a situation in which the Pesul of "Chutz l'Mekomo" does not apply -- in the case of a Bamah. At a time when one is permitted to build a private Mizbe'ach and offer Korbanos upon it, there is no limit to where the Korban must be eaten. That allowance, therefore, is an exception to the Pesul of "Chutz l'Mekomo" and the Pesul is "Hutrah mi'Klalo." (Even though there is no such exception to the Pesul of "Chutz l'Zemano," the Beraisa mentions it merely because it is always mentioned together with "Chutz l'Mekomo.")
2. TOSFOS suggests another answer. Perhaps the Pesulim of "Chutz l'Zemano" and "Chutz l'Mekomo" also have exceptions, since they do not apply to the Minchas Kohanim (the Minchah offering brought by a Kohen) and Minchas Nesachim (the Minchah offering brought with the Korban Tamid). Those offerings are entirely burned upon the Mizbe'ach, and thus they have no Pesul of "Chutz l'Zemano" or "Chutz l'Mekomo."
3. The SEFAS EMES in Yoma (7a) answers that there is no Pesul of "Chutz l'Zemano" or "Chutz l'Mekomo" for Korbanos offered by Nochrim, and that is why they are considered to be "Hutrah mi'Klalo." (This point is subject to a dispute between Rebbi Shimon and Rebbi Yosi in Temurah 2b.)
4. RABEINU PERETZ here answers as follows. A Korban Chatas may be eaten only within the confines of the Azarah, and only for one day. A Korban Shelamim, in contrast, may be eaten throughout all of Yerushalayim, and it may be eaten for two days. Accordingly, although a Korban Chatas becomes Pasul if one has a thought to eat it outside of its proper time (after the first day) or outside of its proper place (the Azarah), such thoughts are considered "Hutrah mi'Klalo" because they are permitted for a Korban Shelamim.
5. TOSFOS in Yoma (7b, DH Ha Eino) says that, indeed, the Pesulim of "Chutz l'Zemano" and "Chutz l'Mekomo" are not "Hutrah mi'Klalo." There are no exceptional cases in which they are permitted. Nevertheless, the Gemara suggests that the Tzitz is Meratzeh for them even though they are not "Hutrah mi'Klalo" because of a Gezeirah Shavah. The word "Avon" is mentioned with regard to the Tzitz (Shemos 28:38) and with regard to "Chutz l'Zemano" and "Chutz l'Mekomo" (Vayikra 7:18).