Why Aaron Brought a Calf and the Golden Calf Atonement

Midrash Tanchuma Buber, Shmini 6:1

(Leviticus 9:2:) "And he said to Aaron: Take for yourself a calf." Why was it not said to him "a bull," but rather "a calf"? He said to him: Because by means of the calf the priesthood was made to totter in your hand, and by means of the calf it is now made firm in your hand. And not only that, but so that Israel should not say there are iniquities upon them from the deed of the calf, therefore He said they should offer a calf, as it is stated (Leviticus 9:3): "And unto the children of Israel you shall speak, saying: Take a male goat for a sin offering, and a calf," and so forth, so that they would know that they had been atoned for regarding the deed of the calf. The Holy One, blessed be He, said to them: In this world they have been atoned for by means of offerings, but in the world to come I will pardon their iniquities without an offering, as it is stated (Isaiah 43:25): "I, even I, am He who blots out your transgressions for My own sake, and your sins I will not remember."

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