Question: "Why was it bad that Aaron and his sons burned the sin offering in Leviticus 10:16-20?"
Answer: Due to the disobedience of Aaron’s sons Nadab and Abihu, the Lord caused those two men to die. Later that day, Aaron and his remaining sons allowed the sin offering to burn up. Moses was angry with Aaron’s other two sons, Eleazar and Ithamar, as a result. This situation is hard to understand until we take a closer look at the context and the Law in general.
For one thing, Moses had just commanded Aaron and his remaining sons to eat the offering (Leviticus 10:12–14). When he discovered they had let it burn up, he was understandably upset.
Also, the chapter opens with the death of two of Aaron’s sons: “Aaron’s sons Nadab and Abihu took their censers, put fire in them and added incense; and they offered unauthorized fire before the Lord, contrary to his command. So fire came out from the presence of the Lord and consumed them, and they died before the Lord” (Leviticus 10:1–2). Likely due to their grief over the deaths of Nadab and Abihu, Aaron and his sons Eleazar and Ithamar chose to let the sacrifice burn up rather than to eat it. Moses was upset because this was breaking the command God had given the priest to use this offering in part as their food.
Another reason Moses was upset was probably that he feared a fate similar to that of Nadab and Abihu would befall Aaron, Eleazar, and Ithamar. He confronted Aaron, saying, “Why didn’t you eat the sin offering in the sanctuary area? . . . You should have eaten the goat in the sanctuary area, as I commanded” (Leviticus 10:17–18).
Aaron’s response to Moses is full of pathos: “Today my sons presented both their sin offering and their burnt offering to the LORD. And yet this tragedy has happened to me. If I had eaten the people's sin offering on such a tragic day as this, would the LORD have been pleased?” (Leviticus 10:19, NLT). These words satisfied Moses that Aaron was living in fear and obedience to God (verse 20).
Interestingly, this passage of Leviticus concludes the section in which Aaron and his sons are inducted as priests before the Lord (chapters 8—10). Occurring over an eight-day period, these events help delineate the important, sanctified role belonging to the Levitical priests.