There is more to Leviticus 10 than the death of Nadab and Abihu! We’re told more so we can place the event in context. It is to our detriment when we ignore this.
After Nadab and Abihu’s relatives were summoned to carry their bodies away, Moses tells Aaron and his remaining sons that they are not to mourn or you will die and the Lord will be angry with the whole community (v.6). Instead, they were to continue their service at the tabernacle (v. 7). This reinforces the importance of what they were doing and minimizes the focus on Nadab and Abihu’s actions. God had manifested His wrath against their sin and they were to uphold His judgment by continuing on. The sin of the two wasn’t to carry the day. This had to have been an enormously difficult thing for Aaron and his sons to do, but they obeyed. Something of the same thing happened with the prophet Ezekiel when his wife died and he was told not to mourn (Ezekiel 24:15-18).
But the day wasn’t over. There was something else that happened that was of significance. Like Nadab and Abihu, Aaron and his sons failed to observe one of God’s commands. Specifically, they did not eat the the sin offering as they were supposed to (v. 17-18). Instead, it was burned (v. 16). In the context of the day’s events, this is amazing. Two sons had already been lost by Aaron because of their disobedience and now the rest of them stood before God guilty of a similar charge!
Aaron’s explanation in v. 19 is worth noting. He pointed out they had obeyed God in all other things, but in light of what had happened to his sons he was not sure if God would have been pleased by their eating. Unlike Nadab and Abihu, it wasn’t insensitivity that brought about their actions but sensitivity! Moses (acting as God’s spokesman), accepted their explanation.
But we shouldn’t miss the point. They didn’t pay for their omission with their lives because they were good (had honorable motives), because Moses’ initial response seems to indicate God didn’t see things the way they did and He expected them to eat the sacrifice. No, their lives were spared because God was and is merciful. On a day of severe judgment there was also mercy. On a day when callousness toward God was punished, the desire to honor God (though expressed incorrectly), was upheld. We’re moved to honor our Father (not just to escape His wrath) because we love Him due to His great mercy toward us in Jesus Christ. It’s the kind of thing Paul is talking about when he writes, God, who is rich in mercy, made us alive with Christ even when we were dead in transgressions—it is by grace you have been saved (Ephesians 2:4-5). That’s the message of Leviticus 10! That’s a healthy sense of the holy.