How can there be a custom which creates Nosar?

Question

The Torah says not to leave over the meat of the Pesach offering (Exodus 12:10), known as the prohibition of Nosar. Even though this prohibition doesn't get lashes, either because it doesn't have an associated action or because it's given over for positive rectification (לאו הניתק לעשה) (Makkos 4b), my (hopefully reasonable) premise is it's still prohibited.

This means that all edible meat has to be eaten. However, this makes the following statement of the gemarra regarding the gid hanashe (sciatic nerve) problematic:

Pesachim 83b, Chullin 91b:

שמנו מותר וישראל קדושים הם ונוהגין בו איסור

How could there be a custom not to eat the fat of the gid hanashe, if it's permitted to eat? If it's permitted to eat, then it should be prohibited not to eat it.

Similarly, the gemarra gives cases where Chazal prohibited certain parts of the animal. If it's actually permissible to eat, they're creating Nosar! Perhaps we have to come on to עקירת דבר מן התורה בשב ואל תעשה, but that won't help for a custom.

Answer 1

Minchat Chinuch 8 suggests that maybe the prohibition to leave over from the korban only applies to those parts of it which are fit to be eaten. The fat of the gid hanashe is not fit to be eaten (due to custom) and therefore the prohibition to leave over does not apply to it.

However, he ultimately moves away from this approach, as it is diffcult to understand why these fats would have to be burned on the sixteenth of Nissan if they are not considered notar.

Instead he believes (as you mentioned) that Chazal removed the prohibition to leave over in the case of these fats, through the mechanism of yesh koach b'yad chachamim la'akor davar min hatorah b'shev v'al ta'aseh.

Answer 2

In fact, the Chofetz Chaim (Likkutei Halachos, Pesachim) is quoted to the effect that the custom can't override the mitzvah, and that the fat should be eaten. (The relevant volume of Likkutei Halachos doesn't seem to be available on Hebrewbooks, unfortunately.)

ומשמע מהרמב״ם דא״צ רק לשייר הגיד ולא השומן,‏ דמותר לאכול שמנו של גיד בקדשים,‏ דאין מנהג בזה לעבור על בל תותירו,‏ ולבטל מ״ע דאכילה,‏ דהא סתם הרמב״ם ולא פירש כלל,‏ רק כתב שישליך גיה״נ וקרומית ותו לא

The Rambam seems to imply that we need to leave over only the nerve itself, not the fat, and that it's permissible to eat the fat of the gid hanasheh of sacrifices, since a minhag can't allow us to violate the mitzvah not to leave anything over, or to abrogate the positive mitzvah to eat it. After all, the Rambam speaks in generalities, without specifying anything beyond that one has to dispose of the gid hanasheh and the [forbidden] membranes, nothing else.

(This clearly doesn't comport with the statement in Pesachim 83b quoted in the question, that the fat can't be eaten. The above sefer goes on to quote R' Yosef Corcus, that the Rambam may understand Ravina in the Gemara there to be disagreeing with Rav Ashi. As for Rav Ashi, then, he might agree with the Minchas Chinuch quoted in Joel's answer, or with the answer below.)

On the other hand, Shiurei Mikdash David (Pesachim, sec. 6) suggests that so long as a person doesn't consider something food (even if, for example, it's just because he's finicky), then halachah considers that dispositive, and he's not required to eat it. (Although, since objectively it is food, it has to be burned with the rest of the nosar.)

In a comment, DoubleAA suggested that this last point might be implied in the Rambam's phrasing וצריך אדם להשתדל ("a person has to make an effort" not to leave anything over, implying something less than a full-fledged obligation). On the other hand, I see where there are various other explanations of what this phrasing implies.