On a de'oraita (Torah law) level, if a korban (offering) gives birth, that baby animal also has the same status as its mother. It has to be brought in the same way as a korban. Here we'll talk about a machloket (dispute): whether the hachamim (the rabbis) prohibited that child, that baby animal, from being brought as a shelamim offering. The Mishnah says: These two rabbis testified that the offspring of a shelamim should be brought as a korban shelamim. They needed to teach this because Reb Eliezer taught that the offspring of a shelamim should not be brought as a shelamim because of the rabbis, under deRabbanan (rabbinic) law.
He says that the rabbis were nervous. He says that if the owner of a shelamim waited for the animal to give birth so that he could now have more shelamim, that waiting period would eventually cause him to forget that the animal was sacred in the first place. Then he may use the animal for work, or he may use its wool, both of which are not allowed. So the rabbi said, “We want to make sure that the korban is brought immediately.” To ensure that, they said that the animal that gives birth to the child, the baby animal, has to die. It has to be left to die, so people wouldn't have any motive to allow the shelamim to wait around. They wouldn't delay. They would bring the korban right away. But the hachamim said that it should be brought as a shelamim. Reb Yehoshua and Reb Papias both gave testimony that the ruling of the hachamim is correct.
Amar (said) Reb Papias: “I testify that we had a cow that was a shelamim offering, and we ate it during the holiday of Pesach. And we ate its child, the baby animal it gave birth to, as a shelamim on the Chag, on the holiday of Shavuot.” Even though Chag usually means Sukkot, here in this context it can't mean that, because the obligation to bring the korban has to be on the next Yom Tov (holiday). So if it gave birth over here, right around Pesach, the next holiday would be Shavuot.