Why do we burn Tamei and Passul Karbanos Pesach on the 15th?

Question

The Mishnah in Pesachim (82a,83a) states:

הפסח שיצא או שנטמא ישרף מיד. נטמאו הבעלים או שמתו תעובר צורתו וישרף בט״ז. ר׳ יוחנן בן ברוקה אומר אף זה ישרף מיד לפי שאין לו אוכלין. העצמות והגידין והנותר ישרפו בט״ז. חל ט״ז להיות בשבת ישרפו בי״ז לפי שאינן דוחין לא את השבת ולא את היום טוב.

A Pesach which left [Yerushalayim] or became tamei is immediately burned. If the owners became tamei or died, we leave the Karban over and burn it on the 16th. R’ Yochanan Ben Beroka said, even in this case it’s burned immediately, since there are no eaters. Bones, sinews, and leftover Karbanos are burned on the 16th. If the 16th fell on Shabbos, we burn it on the 17th, since it doesn’t push off Shabbos nor Yom Tov.

When I learned these Mishnayos with my 10-year-old Chavrusa, he asked me a very simple question, which I was kind of embarrassed that I didn’t come up with on my own.

The Halacha follows Rav (Gemara on 6a) that one who found Chametz on Pesach should cover it and burn it on Chol HaMoed (OC 446:1). Thus, he posed a simple Kal v’Chomer: if Chametz, which has a prohibition against owning it, we still wait to burn it, a Tamei Karban Pesach, which does not have a prohibition against owning it, is it not logical that we should wait to burn it? So why in the beginning of the Mishnah does the Tanna Kamma say that we burn it immediately?

Then we read a bit further and got to the end of the following Mishnah, which said that it doesn’t push off Shabbos and Yom Tov, further strengthening his question. I checked the Gemara, and indeed, 84b-85a gives not one but four different sources that this is the case (Chizkiya’s source that the passuk has an extra “ad boker,” Abaye’s source of “olas Shabbas biShabbato,” Rava’s comparison to a Bris Milah that was pushed off, and Rav Ashi’s understanding that this is an aseh versus an aseh and a lav). Even if his Kal v’Chomer fell apart, he has a Mishnah, defended by several pesukim, that support his question!

I originally thought to answer that Nosar, the subject of the end of the Mishnah, is different than a Tamei or Passul, the subject of the beginning, but then I saw that these same expositions appear in Shabbos 24b-25a regarding the Mishnah of אין מדליקין שמן שרפה ביו״ט, we don’t light on Yom Tov with Shemen Sereifah (Terumah oil that’s Tamei and must be burned). Since the same pesukim are applied by Shemen Sereifah and Nosar, there’s clearly no distinction between Tamei and Nosar. Why, then does the Tanna Kamma in our Mishnah in Pesachim learn that we burn a Tamei or Passul Karban Pesach immediately?

Answer 1

R. Ovadiah miBartenura explains that this mishnah is discussing a case where the korban pesach became impure or left Jerusalem on the fourteenth of Nissan. In such a case, it is burnt immediately on the fourteenth of Nissan. It cannot, however, be burnt at any time on the fifteenth, as it is forbidden to burn invalid sacrifices on Yom Tov.

This is in contrast to a case requiring ibbur tzurah, such as the owners all dying on the fourteenth of Nissan after the korban pesach had been brought. In such a case, it cannot be burnt until it has become notar (on the morning of the fifteenth). And, since the fifteenth is Yom Tov, one must wait to burn it until the morning of the sixteenth.

Answer 2

Partial answer, for reasons to be explained at the very end.

Tosfos (Pesachim 83b “Litein boker sheini lisereifaso”) ask: if the passuk is specifically adding a second morning, implying that you can’t burn it on the second night, how can we derive over in Shabbos that we can’t burn Shemen Sereifah on Yom Tov night? They answer that the real prohibition learned from here indeed is regarding Yom Tov day, and we find elsewhere (Pesachim 3a) that even Shelamim which become Nosar on the third night still are only burned the following morning. We see from here that Kodshim can’t be burned at night.

The Tiferes Yisrael (Yachin §43) adopts this same approach. Therefore, he says, the Mishnah must be talking about a case where it was taken outside when it was still the 14th, and so there’s no problem with burning it immediately.

So this is all well and good if you learn like Chizkiya. The problem is according to the others.

Perhaps you can argue the same in Rava, similar to how a Bris Milah can’t be performed at night. Perhaps you can argue the same in Abaye, similar to how an Olah can only be brought in the morning. But according to Rav Ashi, the approach adopted by the Bartenura to our Mishnah, the question still stands: that an aseh can’t push an aseh and a lav doesn’t matter whether it’s a daytime or nighttime mitzvah, and so according to him, the question should still stand.

Answer 3

The fundamental difference is that there's no mitzva to burn chametz - בביטול בעלמא סגי, just revoking ownership gets you out of the prohibition, and the burning is a Rabbinical addition in case one find a גלוסקא יפה, delicious cake, and eats it before remembering it's Pesach.

However, burning נותר is a mitzva, not a precaution.