Leviticus 21:2
But for his kin, that is near unto him, that is, for his mother, and for his father, and for his son, and for his daughter, and for his brother, But for his kin, that is near unto him, that is, for his mother, and for his father, and for his son, and for his daughter, and for his brother,
Priests were forbidden to defile themselves by taking part in the customs of burial and mourning for the dead, except for their nearest kin — mother, father, son, daughter, and brother. That restriction required them to show full acquiescence in the Lord's judgment. In the case of Nadab and Abihu even that family exception was set aside because of the heinousness of their offense.
Aaron and his remaining sons therefore could make no outward show of mourning for them, nor follow the bodies out, nor attend the funeral. Kinsmen outside the priesthood had to bury the dead priests in their polluted priestly robes. This was because the holy anointing oil upon consecrated priests cannot be associated with mourning, especially for gross desecration of the anointing.