Temurah and Mitzvah HaBah B'Averirah

Question

Masechet Temurah discusses what happens if one makes a temurah -- attempting to designate a replacement for a dedicated offering. Though this is not allowed, the kedushah of the original does (in many cases) fall on the replacement and the person is obligated to offer the replacement as a sacrifice.

On 20b there is an objection to one particular instance, a person cannot receive atonement through the temurah offering because "דאין אדם מתכפר בדבר הבא בעבירה" a person cannot get atonement through committing a sin (making the temurah exchange).

But if the temurah is inherently a sin, how can anyone, in any case offer it as a sacrifice -- isn't offering a sacrifice a mitzvah (according to the list of 613, many parts of the service are discrete mitzvot). Even simply offering the temurah as a consequence is, in and of itself a mitzvah (in at least a rabbinical sense).

Shouldn't this answer of "a mitzvah that comes about my means of committing a sin" excuse a person from having to offer any temurah as a sacrifice? Or does he offer it and somehow it isn't fulfilling any mitzvah and the action is only a punishment? If one eats any of the temurah and makes a bracha, wouldn't this be a bracha whose fulfillment comes because of the sin?

Does the concept of mitzvah haba b'aveiragh not apply here? If so, then why does "ein adam mitkaper"?

Answer 1

The Shela, in Sefer Bigdei Yesha in Succah 33A, mentions in passing that bringing a temuras olah and shlamim is not considered a mitzvah.

(Additionally, he says that the reason a temuras chatas can’t be used is a special Halacha specifically for chatas since it’s being brought to atone for an aveira, it can’t be that you use a different aveira to remove the first one. Based on this, perhaps one can say a lomdishe answer - the aveira of making a temura is an aveira on the person for doing it, but it doesn’t transfer to the animal. The animal isn’t the thing that has the aveira done do it, all it has is the hekdesh, the aveira was the words that the person spoke. Therefore it’s not connected to the mitzvah/korban that is brought later. The only problem with this is that the Gemara says that chatas is an aveira, which seems to indicate that the animal itself is part of an aveira. However, based on this explanation of the Shelah, the issue by chatas is a separate reason of removing one sin through another. If so, there’s no proof that the animal became the part of the aveira and the idea that the aveira is only in the words may still be true).