Commentary for Leviticus 7:8

עור העלה אשר הקריב לכהן לו יהיה [AND THE PRIEST THAT OFFERETH ANY MAN’S BURNT OFFERING] EVEN THE PRIEST SHALL HAVE TO HIMSELF THE SKIN OF THE BURNT OFFERING WHICH HE HATH OFFERED — thus excluding the טבול יום, the מחוסר כפורים and the אונן (cf. Rashi on v. 7) — that these have no share in the skins of burnt offerings (Sifra, Tzav, Chapter 9 5; Zevachim 103b).

AND THE PRIEST THAT OFFERETH ANY MAN’S BURNT-OFFERING, EVEN THE PRIEST SHALL HAVE TO HIMSELF THE SKIN OF THE BURNT-OFFERING. This law applies to all offerings, and although Scripture mentions only the burnt-offering, it holds good of the sin-offering and guilt-offering mentioned above.⁷⁴Above, Verse 1 (the guilt-offering) and 6:18 (the sin-offering). Such is not the case, however, in reference to the peace-offerings [the skin of which belongs to the owner]; therefore Scripture mentioned the law of the priests’ due in the middle of the offerings, before it speaks of the peace-offerings [further on in Verses 11-21].
The interpretation of the Rabbis as found in the Torath Kohanim is as follows:⁷⁵Torath Kohanim, Tzav 9:2. “[From the verse here] I know only that the skin of the burnt-offering [belongs to the priest]. Whence do I know that the same law applies to the skins of [the other] most holy offerings? Scripture therefore says, that offereth. Or perhaps I might think that I am to include [also] the skins of the offerings which are holy to a lesser degree [such as the peace-offering etc.]; Scripture therefore says, burnt-offering, thus teaching that just as the burnt-offering is distinguished by being of the most holy degree of offerings, [so also this law holds good of all most holy offerings], thus excluding those which are holy in a minor degree.”
By way of the plain meaning of Scripture, it was not necessary to state this law [that the skin of the animal belongs to the priest] in connection with the sin-offering and guilt-offering, since they are part of the gifts given to the priests,⁷⁶Numbers 18:9. and the priests thus are entitled to the meat and also the skin, but in the case of the burnt-offering [where the priests do not receive any of the meat, since it is wholly burnt on the altar], it was necessary for Scripture to say that they do acquire the skin. This is the interpretation of Rabbi [Yehuda Hanasi] who says,⁷⁷Zebachim 103 b. “Essentially we need this verse only for the skin of the burnt-offering [to teach that it belongs to the priest], since the skin always follows the meat”⁷⁸“The bullocks which are burnt and the he-goats which are burnt [outside the camp], their skins are burnt with them, as it is said, and they shall burn in fire their skins, and their flesh (further, 16:27) (Torath Kohanim, Tzav 9:5). Hence the Torah had to explain that the burnt-offering is different; but in the case of the sin-offering and the guilt-offering, it was not necessary to mention that the skin belongs to the priest, for since he acquired the right to the meat, the skin naturally came with it. [and here Scripture tells us that it is not to be burnt with the meat]. So also is it explained in the Torath Kohanim.⁷⁸“The bullocks which are burnt and the he-goats which are burnt [outside the camp], their skins are burnt with them, as it is said, and they shall burn in fire their skins, and their flesh (further, 16:27) (Torath Kohanim, Tzav 9:5). Hence the Torah had to explain that the burnt-offering is different; but in the case of the sin-offering and the guilt-offering, it was not necessary to mention that the skin belongs to the priest, for since he acquired the right to the meat, the skin naturally came with it.

עור העולה אשר הקריב, לכהן לו יהיה, “the skin of the burnt offering which he presented shall belong to the priest who performed this procedure.” Although this legislation is spelled out only in connection with the burnt offering, the same rule applies to the skins of sin-offerings or guilt-offerings. However, the skin of peace-offerings,זבחי שלמים, belong to the respective owners of the sacrificial animals, not to the priest. Some sages claim that there had been no need for the Torah to spell out that the skins of sin and guilt offerings also belong to the officiating priest, seeing that even a substantial part of the meat of these offerings belongs to the priests. It is natural that the skin, something secondary, always belongs to the party to whom the flesh belongs. Seeing that no meat of the burnt offering belongs to the priest, the Torah had to specifically state that at least the skin does belong to the officiating priest.

והכהן המקריב את עולת איש, “and the Priest who offers a person’s burnt-offering, etc.” the word: “the Priest” does not apply exclusively to one individual Priest, suggesting that his colleagues on duty on that day do not have a share in that hide. The word has to be understood in the same vein as the word המחטא in 6,19 where we already explained that the Priest in question is not the only one eating of that sacrifice. The words הכהן המקריב apply to any Priest who is in a fit state to perform the service at that time, i.e. the Priests of that roster. [There were a total of 24 rosters of Priests who performed the Temple Service in rotation. Ed.] Anyone of that roster who was ritually impure at the time was excluded from participating even in receiving part of the hide. The reason that the Torah adds the words אשר הקריב, “which he had offered,” words which appear superfluous, is that the entitlement to the hide does not begin until after the procedures of offering the animal have been completed, not at the time when the hide was removed from the carcass. If, for argument’s sake, it was discovered after the animal in question was slaughtered that it was diseased and not fit for burning up on the altar, the Priest has no claim to the hide. The same holds true if other errors occurred in the procedure such as the blood being spilled, etc. (compare Zevachim 103).
Our sages say that all the animals underwent a physical examination prior to being slaughtered in order to minimize the chance of blemishes being found later. Even minor blemishes in the eye of animal were minutely examined at that time [to determine if this was a temporary or permanent blemish. Ed.] This is alluded to in the words “which he had offered,” meaning that after the examination the Priest had thought himself as entitled to that hide (Compare Maimonides’ comments on Erchin 2,5).

A מחוסר כפורים. Meaning: Sometimes there is an impure person [that has entered the mikveh] who needs to bring a sacrifice the next day.

והכהן המקריב, “and the priest who offers, etc.” The singular mode used here for “the priest,” is misleading, as it includes all the priests belonging to this particular watch, i.e.doing service on that day. All of them are described by the Torah as כהן. (Karney Or)

Who do not share. Excluding a טבול יום. Even though Scripture excluded them from a share in the meat, as stated above (v. 7), I might think that specifically with regard to the meat, which is eaten, and these kohanim are not fit to eat now — therefore, Scripture excludes them. Regarding the skins, however, since they are not fit to be eaten, I might think that although these kohanim are not fit for performing service, nonetheless they share in the skins. Therefore, it lets us know ... [that since they are not fit for performing service or eating,] they are excluded from sharing in the skins.