1. Moshe, I can take a quick shot at answering this interesting question based on the Hasagos ha'Ra'avad on the Rambam, Hilchos Bikurim 12:1. The Ra'avad writes that there is no Mitzvah, in its own right, of doing Arufah on the first born of the donkey if one does not want to redeem the donkey on a sheep. The Ra'avad learns that when the Torah states, "And you shall redeem the first born of the donkey on a sheep; and if you do not redeem it then you shall do Arufah" (Shemos 13:13), this means that the only Mitzvah is to redeem it on a sheep. However if one does not want to do this Mitzvah, there is no choice but to destroy the donkey by doing Arufah. The Ra'avad writes that it contradicts correct logic to suggest that Arufah is a Mitzvah. On the contrary, he writes it is a transgression to destroy the Peter Chamor in such a way. It is considered as damaging, and of causing the Kohen a loss because the real Mitzvah is to give a sheep to the Kohen.

However, it must be conceded that the Rambam there does consider the Arufah of a Peter Chamor to be a positive Mitzvah, so we will still have to think of an answer to explain the Rambam's opinion, bs'd.

2. A simpler answer:

A much more straightforward way of answering this question is to note that the Gemara expounds a Derashah to say that the only Arufah is the Eglah Arufah; but this Derashah cannot override an explicit verse in the Torah that one can do Arufah on the firstborn of the donkey. Therefore, we must say that this Derashah -- that the only Arufah is Eglah Arufah -- is referring only to situations where it does not say clearly in the Torah that one can do Arufah. An example is the Parah Adumah, where the Torah prescribes slaughtering, but does not say anything explicit about Arufah. For this, the Gemara cites the verse "ha'Arufah" (Devarim 21:6), which Rashi here (DH ha'Arufah) explains to be a "Mi'ut" -- only Eglah can have Arufah, but Parah Adumah cannot.

According to this, we must say that when the Gemara states "and another does not have Arufah," it refers only to Dinim for which it is not stated clearly in the Torah that there is Arufah. Therefore, the Gemara is referring only to Parah Adumah and not to Peter Chamur.

This answer can work according to both the Rambam and the Ra'avad.

Yasher Ko'ach,

Dovid Bloom

Even according to the Rambam that Rav Bloom mentioned (in answer 1), who learns - like most other Rishonim - that Arifah is a Mitzvah, nevertheless it is clear that the Mitzvah of Arifah is only b'Di'eved since l'Chatchilah one must be Podeh the Peter Chamor, as the Mishnah states at the end of the first Perek of Bechoros. Thus, the Gemara here might be saying that the only place where Arifah is performed l'Chatchilah is by Eglah Arufah, and this implies that it is not to be performed by a Parah Adumah. (Parah Arifah cannot be done even b'Di'Eved, since we never find that Arifah is allowed b'Di'eved in a case which requires Shechitah l'Chatchilah.)

Yasher Koach again for the interesting question!

Mordecai Kornfeld

Kollel Iyun Hadaf