The principle of “Ein kategor na’aseh sanegor” (“A prosecutor cannot become a defender”) means that items which contributed to Jews sinning cannot be used as part of the divine service to bring the Jews atonement. Thus, the Rosh Hashanah shofar is not made from the horn of a cow, because it brings to mind the sin of the Golden Calf. However, according to the Talmud, this principle is limited to articles that were used for the divine service in the Temple (such as a shofar, which was blown there daily). Thus, the Parah Adumah (Red Heifer) could be used to atone for the sin of the Golden Calf, since the ceremony involving it took place outside the Temple.
If this is correct, why can’t a Kohen who committed murder recite the priestly blessing? Tosafot (Yevamot 7a) suggests that the reason he is excluded is “Ein kategor na’aseh sanegor.” But this blessing is recited outside the Temple, so he should be permitted to do so! It would seem that outside the Temple, what is permitted for the divine service is the use of an object (such as gold or a cow’s horn) even though it might bring to mind a certain sin. In contrast, the sinner himself (such as a Kohen who committed murder) may not perform the divine service, even outside the Temple.
If this is correct, how do we explain the command to Aharon to take a calf during the eight days of the dedication of the Tabernacle (Vayikra 9:2)? Rashi answers that this was done to indicate that G-d had forgiven the Jewish people for the sin of the Golden Calf. But based on what we just said, a calf itself should not have been allowed! It would seem that when asking forgiveness for a specific sin, the chance of true repentance increases when the very item which was used to commit the sin is used for atonement. This is why the gold donated to make the Tabernacle was able to atone for the gold which people had enthusiastically donated to make the Golden Calf.