The source brought by Bet Shammai is the passage in Sefer Bamidbar (18:17-18) where the firstborn animal is compared with the hazeh ve-shok – parts of sacrifices that can only be eaten by kohanim. Bet Hillel argues that that pasuk (=verse) refers specifically to an unblemished firstborn that was brought as a sacrifice. The passage that is appropriate for our case appears in Sefer (15:19-22) where the blemished firstborn is compared to a tzvi and an ayal – wild animals that are kosher and can be eaten by all.
When the Torah requires that gifts be given to kohanim and levi’im, some (e.g., terumah) are considered sanctified and may not be eaten by anyone aside from a kohen, while others (e.g. ma’aser) are simply the monetary property of the recipient and can be eaten by anyone.
Where does a firstborn animal stand regarding this question? If the animal is sacrificed, then clearly the sanctified parts are kodashim and must be eaten within the Temple precincts only by kohanim. The question is relevant, however, when the firstborn animal develops a mum – a blemish – that precludes it from being sacrificed. In that case, may the kohenshare the meat with others, or is it restricted in a fashion similar to that of terumah?
The Mishnah on today’s daf (=page) and the baraita that follows, deal with this question. According to the Mishnah, there is a disagreement between Bet Shammai and Bet Hillel on this point. Bet Shammai say that an ordinary Jewish person may not be invited to share a blemished firstling with a priest, whereas Bet Hillel permit both a Jew and a non-Jew to share in the meat. According to the baraita, Bet Hillel permit an ordinary Jew to partake, and it is Rabbi Akiva who permits even non-Jews to eat the meat of a firstling.