The Torah in Parashat Emor (22:22-24) lists a number of physical defects that disqualify an animal for use as a sacrifice. The Gemara in Masekhet Bekhorot (37a) establishes that these defects enumerated in the Torah are not the only blemishes which disqualify an animal, as any blemish which resembles these features renders an animal unsuitable as a sacrifice. Specifically, a physical blemish which is both visible and permanent (“mum she-ba’galui ve-eino chozer”) disqualifies an animal.
One of the examples given by the Mishna (Bekhorot 39a) is an animal whose external “chutin” are cracked or broken, and an animal whose inner “chutin” have been lost entirely. There is a debate among the Rishonim as to the definition of the term “chutin.” Rabbenu Gershom (Bekhorot 35a) defines the word as a reference to teeth, and thus in his view, an animal whose teeth have fallen – or even whose front teeth, which are readily visible, are cracked – is unsuitable as a sacrifice. Rashi (35a) and Tosefot (37a), however, explain “chutin” as referring to the animal’s gums. According to this view, then, tooth loss does not render an animal disqualified for use as a sacrifice.
Tosefot draw proof to their position from the Mishna later in Masekhet Bekhorot (44a) which establishes that a kohen who has lost his teeth is disqualified from serving in the Beit Ha-mikdash only because of mar’it ha-ayin – the concern that this would appear unseemly. As the Gemara noted earlier (43b), the disqualifications that apply due to mar’it ha-ayin were enacted by Chazal, and do not apply on the level of Torah law. This means that according to Torah law, a kohen who lost his teeth is allowed to perform the service in the Mikdash. Tosefot thus reason that if the absence of teeth does not constitute a blemish for a kohen, it should likewise not constitute a blemish for an animal which one wishes to offer as a sacrifice. Necessarily, then, when the Mishna disqualifies an animal that has lost its “chutin,” it cannot refer to teeth. Tosefot therefore follow Rashi’s view, that “chutin” refers to the animal’s gums.
In defense of Rabbenu Gershom’s view, the Tiferet Yisrael commentary to the Mishna (Bekhorot, Yakhin 7:45) suggests that the loss of teeth is considered a blemish for animals because they frequently open their mouths wide and expose their teeth. If an animal lost its teeth, then, this blemish would be very obvious and evident, and it therefore constitutes a mum, a disqualifying physical defect. Human beings, by contrast, do not frequently open their mouths in a manner that exposes their teeth, and thus the loss of teeth does not constitute a mum (on the level of Torah law).
Rav Avraham of Sochatchov, in his Avnei Neizer (O.C. 131:5), offers a different line of reasoning to defend Rabbenu Gershom’s view. He notes that whereas kohanim are eligible to serve in the Beit Ha-mikdash at any age, an animal becomes disqualified for use as a sacrifice once it reaches three years of age (Para 1:2). Tooth loss is a normal, natural part of aging, the Avnei Neizer writes, and therefore it does not constitute a defect for a kohen, since even aged kohanim may perform the service. For animals, however, it indeed constitutes a defect, since only young animals are suitable as sacrifices, and thus tooth loss for an animal is unusual and treated as a disqualifying blemish.