What did Aaron have to offer for himself on the Day of Atonement?
Aaron had to offer his bullock as a sin offering for himself and his house. He killed this first sacrificial animal to make atonement for himself and his family, because even as high priest he was a sinner and needed cleansing before beginning the Day of Atonement.
Les explains that on the Day of Atonement Aaron could not begin his high priestly role until he first washed thoroughly and put on the linen undergarments and holy garments. Then, after taking the two goats and the ram for the congregation, verse 6 says Aaron had to offer his bullock of the sin offering for himself and make atonement for himself and his house. Even though he was Israel's high priest, he was a sinner just like anyone else, so he had to kill this first sacrificial animal for himself and his family. Only then could he take the blood and proceed further in the ritual, including taking coals and putting them on the altar of incense, where the smoke served as his covering.
And Aaron shall offer his bullock of the sin offering, which is for himself, and make an atonement for himself, and for his house.