Bechorot 33 - Whom Can a Kohen Invite to Eat a Firstborn Animal?
Previously we assumed that once a firstborn animal receives a blemish and can't be a sacrifice any longer, anyone can eat its meat. However, Beit Shammai use the Torah phrase, " Their flesh will be yours like the breast of waving ..." - to prove that only the Kohanim can eat it. Beit Hillel say that this phrase applies only to unblemished firstborn. Instead, " the ritually pure and impure can eat it " is applicable here - and a non-Kohen is certainly included, since he can be pure. Beit Shammai answer that the ritually impure cannot be used for any proof, since the Passover offering is brought even when the Community of Israel is impure, but not by a non-Kohen. And Beit Hillel? They answer that this is talking about service, and they are talking about eating.
It is forbidden to inflict a blemish on a firstborn animal. If blood-letting is necessary for a firstborn animal to survive, Rabbi Yehudah still forbids it, since once you permit that, people will inflict other blemishes. They Sages say that if you prohibit bloodletting, people will certainly cause blemishes on purpose, thus the Sages allow blood-letting, but not the slaughter, should the blemish indeed occur.
Art: Camille-Leopold Cabaillot-Lasal - The Pet Lamb