On the 8th day of the inauguration of the Mishkan, Aharon was commanded to offer a personal korban of an eigel (calf) as a chatat (a korban to atone for a sin) and an ayil (ram) as an olah (another type of korban). Then the people offer a goat as a chatat; a calf and a lamb, each as an olah; and a bull and ram as shelamim (also a type of korban). It seems strange that anyone would want to bring a calf as a korban, which might remind G-d of the recent sin of the Golden Calf that the Jews worshipped. What was the purpose of each korban (Aharon’s and the entire nation’s) and the reason for the choice of a calf?
The calves, as nearly all calves in korbanot, are connected to the sin of the Golden Calf, either as atonement for the sin and/or an indication that G-d has forgiven the people for it. In the context of atonement, it is “safe” to remind G-d of the sin. The Golden Calf, in one context called “the calf that Aharon made,” would require a korban from Aharon in atonement. Therefore, the calf on the eighth day is his chatat, since he was guilty of it. The calf of the people is an olah, rather than a chatat. One reason an olah would be brought is not for direct sin but for indirect participation. Chatat is for direct actions. Three thousand Jews participated in the crime of the Golden Calf, and all were killed. The only one remaining to atone for it was Aharon. The rest of Israel was not accountable for the Golden Calf, but were at fault for not taking an active role against it. For this reason they brought a calf as an olah.