Leviticus 10:7 And ye shall not go out from the door of the tabernacle of the congregation, lest ye die: for the anointing oil of the Lord is upon you. And they did according to the word of Moses.
In this instance, Aaron must not even appear to be in sympathy with his sons, nor should he manifest a disapproval at the Divine correction because, as the 2nd prominent leader in Israel he would by so doing convey to the congregation the feeling that God had been unfair in His intervention, and that God went overboard by consuming his two sons during divine hour.
Then the multitudes who would be prone to indulge in false sympathy would join Aaron, and before you know it, the entire congregation will conclude that God was wrong in what He had done. Therefore, by partaking of the spirit of Cain who first accused God of heavy-handedness the congregation would make themselves ripe for destruction.
Parenting children often involves unpalatable duties such as administering correction when it is due. And in some instances, the gravity of the offence would call for a harsher response than in others. Speaking to kids at first is a must, but if over a period of time the desired results are not realized then parents are required to take it up at increasing notches.
Proverbs 29:15 The rod and reproof give wisdom: but a child left to himself bringeth his mother to shame.
May The Lord add His blessing to the study of His word. God bless!