When dealing with an unblemished bechor (firstborn animal) that is brought as a korban (offering), only the Kohanim (priests) and people who are part of their family are allowed to eat the korban. Here, we’ll talk about the meat of a blemished bechor. The Mishnah says: A non-kohen (non-priest) is not allowed to join a kohen and eat a blemished bechor if Yisrael (Israel) was invited by a kohen. He is not allowed to eat from that bechor because the meat is forbidden to non-kohanim.
Beit Shammai learns this from the pasuk (verse) that says, “The flesh should be yours only. Like the breast that’s waved and the right thigh, it should be only yours.” This specifies that it is only for kohanim. Beit Hillel allows a non-kohen to join and eat the meat of a blemished bechor. According to Beit Hillel, even a non-Jew may eat it. The pasuk we just brought is only talking about an unblemished bechor. That’s what it’s talking about; that’s only for kohanim. But a blemished bechor is allowed to be eaten by anybody, as the pasuk tells us: “In your cities you should eat it, a person who is impure and a pure person, like a deer and like an ayal (stag).” So what we learn from here is that anybody is allowed to eat this, just as non-domesticated animals like a tzvi (deer) and an ayal are allowed to eat these. Therefore, a non-Jew is also allowed to eat the blemished bechor.
There’s a prohibition against causing a blemish to any bechor or to another animal that is being brought as a korban. Here, we’ll talk about whether you’re allowed to operate. Are you allowed to do a procedure that may cause a blemish, but you’re doing it to save the life of the bechor? Bechor she'achazo dam, a bechor that had an excess of blood and it was getting sick, and you needed to let some of the blood out. It was a remedy, a bloodletting where you’d cut the vein and let some of the blood out. Even if it’s going to die if you don’t treat it, you’re not allowed to take blood out of it. This is the opinion of Rebbe Yehuda. You’re not allowed to make a blemish anywhere on the animal, even in a place that’s not going to result in a blemish. According to Rebbe Yehuda, people become frantic when they’re faced with a loss of money. So, if we allow the kohen to make a cut in the wound, he may rush to try to save the animal if it is going to heal, and he's going to cut in a place that would cause a blemish. To prevent that problem, which would be a violation of the Torah, we do not let the kohen cut any part of the animal to let blood. But the Chachamim (Sages) say you’re allowed to let blood, as long as you don’t put a blemish into the animal—as long as the cut you make on the animal’s body is in a spot that’s not considered to be a mum (blemish). If you did put a blemish on it while letting blood, the bechor is not allowed to be slaughtered and eaten because of that blemish. Rather, you have to wait until another blemish develops, and then you’re allowed to slaughter the bechor. A person made this blemish with his own hands, so he’s not allowed to slaughter the animal on account of that blemish. You have to wait until another blemish develops. We don’t want you to benefit from the blemish you’re causing.
Rabbi Shimon says that he’s allowed to let blood even if you’re inflicting a blemish on it. You’re allowed to cut anywhere on the body, even if it’s going to cause a blemish. Since the intention here is not to cause a blemish but to cause healing to the animal, you’re not doing an aveirah (transgression). A blemish does happen. As a result of letting blood, the bechor is also allowed to be slaughtered. That’s the third opinion. That’s the third opinion here in the Mishnah of Rabbi Shimon.

