On the inauguration day of the Tabernacle, why Aaron did not eat the goat of the sin offering as instructed by Moses?

[tonychanyt]

Lev 6:

24The Lord said to Moses, 25“Say to Aaron and his sons: ‘These are the regulations for the sin offering: The sin offering is to be slaughtered before the Lord in the place the burnt offering is slaughtered; it is most holy. 26The priest who offers it shall eat it; it is to be eaten in the sanctuary area, in the courtyard of the tent of meeting.

The unstated assumption was to enjoy your meal. Deuteronomy 12:7

There, in the presence of the LORD your God, you and your families shall eat and shall rejoice in everything you have put your hand to, because the LORD your God has blessed you.

On the inauguration day of the Tabernacle, the Lord killed Nadab and Abihu, sons of Aaron for offering strange fire. Later in the day, Lev 10:

16 Now Moses diligently inquired about the goat of the sin offering, and behold, it was burned up! And he was angry with Eleazar and Ithamar, the surviving sons of Aaron, saying, 17“Why have you not eaten the sin offering in the place of the sanctuary, since it is a thing most holy and has been given to you that you may bear the iniquity of the congregation, to make atonement for them before the LORD? 18Behold, its blood was not brought into the inner part of the sanctuary. You certainly ought to have eaten it in the sanctuary, as I commanded.”

Why didn't they?

19And Aaron said to Moses, “Behold, today they have offered their sin offering and their burnt offering before the LORD, and yet such things as these have happened to me!

His two older sons died earlier. He was in mourning. He did not feel like eating.

If I had eaten the sin offering today, would the LORD have approved?” 20And when Moses heard that, he approved.

Gill's Exposition of the Entire Bible:

And Aaron said unto Moses,.... For what Moses had said was said in his presence, though not addressed to him directly, but to his sons; and he was sensible that he was pointed at, and that if there was any blame in this affair, it lay as much or more on him than on his sons; and therefore he takes it upon him to give an answer, and to excuse the fact as well as he could:
behold, this day they have offered their sin offering and their burnt offering before the Lord; that is, the people of Israel had brought a kid of the goats for a sin offering, and a calf and a lamb for burnt offering, and he and his sons assisting him, had offered them for them, even on the very day his two eldest sons were removed by death in an awful manner:

and such things have befallen me; at this very time, soon after the above sacrifices were offered, happened the death of his two sons, which occasioned great anguish and distress, grief and sorrow, so that he could not eat of the sin offering; he had no appetite for it, and if he had, he thought in his present circumstances it would not have been right, as follows:

and if I had eaten the sin offering today, should it have been accepted in the sight of the Lord? he being a mourner. The Jews say (u), an high priest may offer, being a mourner, but not eat; a common priest may neither offer nor eat; and which they illustrate by this passage, that Aaron offered and did not eat, but his sons did neither.

(u) Misn. Horayot, c. 3. sect. 5. Maimon. & Bartenora in ib.

On the inauguration day of the Tabernacle, why Aaron did not eat the goat of the sin offering as instructed by Moses?

Aaron and his two surviving sons felt bad about losing the two older brothers. They could not eat the offering with joy. When Moses heard the explanation, he was satisfied with this exceptional circumstance.