Charles Ellicott Commentary Leviticus 16:11

"And Aaron shall present the bullock of the sin-offering, which is for himself, and shall make atonement for himself, and for his house, and shall kill the bullock of the sin-offering which is for himself:" — Leviticus 16:11 (ASV)

And Aaron shall bring the bullock. — Having formally dedicated the bullock for his own sin offering , and after the two goats that constituted the people’s sin offering had been presented and their lots decided (Leviticus 16:7–10), Aaron comes back to his own sin offering a second time. He again laid both his hands on the victim and repeated the confession for himself, for his house, and for the whole priesthood, as given in Leviticus 16:6.

And shall make an atonement for himself. — His own sins first had to be expiated before he could offer the atoning sacrifices for the people (Hebrews 9:7).

And shall kill the bullock. — Being a sacrifice offered up for himself, the high priest, like any layman, had to slaughter the victim and could not delegate this work to anyone else . He received the blood in the sprinkling bowl, which he handed over to a priest to stir the blood lest it should coagulate while he performed the fumigation.