Commentaire sur Le Lévitique 10:1

ויקחו שני בני אהרן איש מחתתו, they thought that just as after the daily communal offering which was accompanied by the manifestation of G’d’s Presence as we know from Exodus 29,42 עולת תמיד לדורותיכם פתח אהל מועד לפני ה' אשר איועד לכם שמה, “the regular communal burnt offerings for your generations in the presence of the Lord, where I will manifest Myself there,” there would come the incense, so it would also be in order on this occasion to present a new incense offering honouring the manifestation of the Lord to the whole people and in honour of the heavenly fire having descended.

It seems to teach that the place of their error was for two reasons. The first was that in becoming priests, they erred in their service, and this ( is implied in the text) beginning by saying they were 'sons of Aaron'; the two of them (thought) they were great in deeds and should be weighted like Moses and Aaron [Torat Kohanim Achrei Mot 53]. And as the Zohar teaches, they were on a high spiritual level in the realm of deeds, hence they were called ('sons of Aaron') Nadav and Abihu, and this trait is not so for Elazar and Itamar (the Torah does not refer to them as 'sons of Aaron'); they too are 'sons of Aaron', but are not at the spiritual level themselves that Nadav and Abihu were. So too we find this explanation where (the Torah) says

ויקחו בני אהרן נדב ואביהוא, before the fire had emanated from the Holy of Holies they each took his own pan planning to offer incense on the golden altar, seeing that this offering precedes (timewise) the disposal of not totally burned leftovers from the previous day’s sacrificial meat. They placed “alien” fire on these pans, something which had not been commanded by Moses to be done on this day. Even though on ordinary days the rule of “the sons of Aaron will place in these pans fire on the altar” (Leviticus 1,7) was in effect, this rule did not apply to the day of inauguration, and Moses had not wanted any man made fire to be introduced into the Tabernacle. This was because he expected heavenly fire to manifest itself so that the addition of man made fire would have completely ruined the impact of the miracle. On this day the name of G’d would be glorified by all the people becoming aware of Divine approval of their offerings, by G’d accepting same by means of heavenly fire We find a parallel to this in Kings I 18,25 when the prophet Elijah on Mount Carmel ordered the priests not to put any fire on the altar.