Aaron was not to slay the bullock at this time, but was to present it to the Lord at the door of the tabernacle for His acceptance (see v. 11). He left it standing near the altar of burnt offering, ready to offer it when the time should come.
For his house.
This bullock was for himself and his family. He alone was to officiate on this solemn occasion, and must be free from every stain of sin before he could appropriately typify Christ in His mediatorial role (see John 17:19). The other priests assisted, but offered no sacrifice.