Why did Aaron have to kill the first sacrificial animal on the Day of Atonement?

Les explains that before Aaron could begin the Day of Atonement ritual, he had to wash thoroughly, put on linen undergarments, and then put on the holy garments. He was then to take two young goats, one for a sin offering, and a ram for a burnt offering. In verse 6, Aaron first offered his bullock of the sin offering for himself and his house. Even though he was the high priest of Israel, he was a sinner and sinned just like anybody else. So in order to begin this role of the high priest, Aaron had to kill this first sacrificial animal for himself and his family. This contrasts with Christ, who went in sinless even though He took our sin upon Himself. Afterward, Aaron would take the blood of that offering and make his way through, stopping at the laver of cleansing, and he would take coals from off the altar and bring them in to put on the altar of incense, where the smoke served as his protection or covering.