Why did the high priest Aaron have to offer a sacrifice for his own sin first?
Aaron, though the high priest, was himself a sinner who sinned just as anyone else. He therefore had to offer a bullock as a sin offering to make atonement for himself and his household before he could begin his role as high priest.
Les explains that even though Aaron was the high priest of Israel, he was still a sinner and sinned just as well as anybody else. Therefore, before he could begin the Day of Atonement ritual, he had to wash thoroughly, put on linen undergarments and holy garments, and then take two goats, one for a sin offering and a ram for a burnt offering. Verse 6 says Aaron shall offer his bullock of the sin offering, which is for himself, and make atonement for himself and for his house. Only after making atonement for himself and his family could he proceed. This contrasts with Christ, who entered sinless, even though He took our sin upon Himself. Aaron had to kill that first sacrificial animal for himself and his family, then take its blood and the coals from the altar to the altar of incense, where the smoke served as his protection or covering.