Commentary for Leviticus 6:19

המחטא אתה means the priest who performs those rites connected with it (i. e. those connected with the sprinkling of the blood), he is called the מחטא because it is through him that it becomes a sin-offering.

הכהן המחטא אותה יאכלנה, “the Priest who is instrumental in conferring atonement through it, he shall consume it.” The meaning of these words is not that the Priest who sprinkles the blood on the Altar and burns up the fat parts is to be the only one to consume the meat of this offering, and that the other Priests are not to receive any part thereof. If this were so it would lead to friction amongst the Priests as each one would say that he wants to perform the service of the sin-offering. Rather, the meaning of the word המחטא, refers to all the Priests theoretically suitable to perform this procedure, so that only the temporarily ritually impure Priests are excluded by these words. Even Priests who suffer from a brief ritual impurity such as the emission of semen, something that can be purified by sunset, are excluded from eating any part of the sin-offering or guilt-offering offered on the day of their impurity. Neither could they share in the eating of the meal-offerings or be recipients of the chest and upper thigh of peace-offerings which the owners have to give to the Priests.
We know that this rule applies in the case of the sin-offering as the Torah writes הכהן המחטא אותה יאכלנה; the Torah writes in connection with the guilt-offering: הכהן אשר יכפר בו לו יהיה, “it will belong to the Priest who performs the atonement rites on it” (7,7). In connection with the peace-offering the Torah writes (7,14) “the Priest who sprinkles its blood, it shall be his.” In connection with the meal-offering the Torah writes (7,9) “every meal-offering baked in an oven....it shall be the Priest’s who offers it up.” Seeing that all the aforementioned sacrifices are of the category which the Torah described as “most holy,” and may be consumed only on the day they are being offered, anyone who was not ritually pure at that time is automatically excluded from eating part of such an offering seeing it cannot be saved up for the following day.

One fit [to perform] the Temple service. Rashi did not explain the verse according to its plain meaning — “[The kohein] who offers it as a sin-offering, shall eat it” — because it is written (v. 22): “Every male among the kohanim may eat it.” We need not ask: Perhaps the one fit for the avodah shall eat it — to exclude a kohein who has a physical blemish, who is not fit. [The answer is:] It is written: “Every male” — to include a kohein with a blemish. Perforce, it comes to exclude an impure kohein who immersed in a mikveh that day [and could eat it at night] — that he has no share. We should not say: Say the opposite! The one who immersed in the mikveh that day may eat at night, but the kohein with a blemish may never eat. [We do not say this because] it is logical that the kohein with a blemish should partake since he is allowed to eat immediately, and to exclude the one who immersed that day who may not eat until the evening. Meaning: It is impossible to say that it means [only the one who offers] should actually eat it, and the one who was impure at the time of the sprinkling [of the blood], who was not fit for the avodah, will be forbidden afterwards from partaking [in the meat of the offering] at all. Because if so, a minor as well, who was not fit for avodah at the time of sprinkling would be forbidden afterwards to eat. And if you would claim that this is so — [it cannot be, for] we include from “Every male” — even a minor — “may eat it.” Rather, here we only exclude that he [i.e., the impure kohein] may not have a share in the meat (Divrei Dovid).

המחטא אתה יאכלנה THE PRIEST THAT OFFERETH IT MAY EAT IT — i. e., the priest who is fitted to carry out the rite (so that the words denote: Any priest who may offer it as a sin-offering may eat of it; they do not refer to that priest alone who offered it). Thus there is excluded a priest who is unclean (and therefore unfitted) when the blood is sprinkled — that he has no share in the flesh. One cannot say that Scripture here forbids the eating of it to ANY priests (i. e. even to clean priests) except him who sprinkles the blood, because, you see, it is stated later on (v. 22), “All the males among the priests may eat thereof” (cf. Zevachim 99a).