Rabbi Manei of She’av, Rabbi Yehoshua of Sikhnin, and Rabbi Yoḥanan in the name of Rabbi Levi said: Due to four matters Aaron’s sons died, and death is written regarding all of them. Because they were intoxicated with wine, and death is written in its regard, as it is stated: “You shall not drink wine or intoxicating drink, [you, nor your sons with you, upon your entry into the Tent of Meeting, that you not die]” (Leviticus 10:9).
Because they were lacking vestments, and death is written in its regard, as it is stated: “They shall be on Aaron and his sons [whenever they enter the Tent of Meeting…so they will not bear iniquity and die]” (Exodus 28:43). What were they lacking? It was the robe, in whose regard death is written, as it is stated: “It shall be on Aaron to serve…[and he will not die]” (Exodus 28:35). Because they entered without washing hands and feet, as it is stated: “They shall wash their hands and their feet, and they will not die” (Exodus 30:21), and it is written: “When they come to the Tent of Meeting they shall wash in water” (Exodus 30:20).
And because they did not have children, and death is written in its regard; that is what is written: “Nadav and Avihu died before the Lord…and they had no children” (Numbers 3:4). Abba Ḥanin says: It is because they did not have wives, as it is written: “And atone for himself and for his household” (Leviticus 16:6); “his household,” this is his wife.