Shemini:

Aharon’s sons, Nadav and Avihu, each took his pan, put fire into them and placed incense upon it, and they brought near before God strange fire which God had not commanded them.

10:1

The sons of Aharon did not give the proper respect to Aharon. Nadav and Avihu did not take counsel with Moshe; each man took his own pan, each went forth on his own, not even taking counsel with one another.

Torat Kohanim (8^th Century)

To be sure, their intention was praiseworthy. Even after their sin God Himself refers to them as “those near to Me.”…But the fact that, at their moment of greatest delight, when God’s Oneness was demonstrated to the entire nation, they could feel the urge to make a separate offering on their own shows that they were not imbued with the spirit that Judaism requires of its priests. In Judaism, the priest is completely identified with the nation. His position is in no way set apart…

Samson Raphael Hirsch (19^th Century)

Evidently, Nadav and Avihu did not offend against any ritual precepts but sinned by reaching for God through the dictates of their own hearts rather than through the path set by God. Submission to the yoke of Heaven – the ultimate aim of the Torah – was here supplanted by unbridled religious ecstasy. Hence their punishment. It is neither through momentary passion nor even through self sacrifice that the religious goal is attained but rather through the discipline spelled out in the precepts of the Torah. Many consider such submission to the commandments, as against spontaneous worship stimulated by personal and subjective sentiments, as mechanical and objectionable. Yet, we learn…it was precisely the unrestrained desire to ascend to forbidden heights that constituted an unpardonable sin.

Nechama Leibowitz (10^th Century)

There are multiple midrashic attempts to explain the nature of the two sons’ offense. They were inebriated, they were impatient to succeed Moses and Aaron or, more charitably, they were motivated by excessive piety – they wanted to be closer to God. But underlying these accounts runs a common theme…The sanctuary was sacred space. This was where God’s presence was manifest. This was where heaven and earth, the sacred and the everyday met. This was…the center of the world… Its sanctity must be respected. Therein lay the sins both of Nadav and Avihu…they failed to grant proper respect to the sacred. Instead, they trivialized it.

Neil Gillman (contemporary)

Perhaps their sin becomes more comprehensible in the context of the parsha as a whole. This is a parsha that describes its concerns with elaborate and careful detail. This is a parsha that is concerned to delineate boundaries, that defines the sphere of the holy and, by implication, the profane that lies outside. This is a portion that, in its exact description of the sacrificial ritual, its prohibition of priestly drunkenness, and its elaboration of the dietary laws puts “difference between the holy and the common, and between the unclean and the clean.” Perhaps then the sin of Nadav and Avihu lies in innovation, in going outside the boundaries of what id defined in advance as permitted, in rejoicing in the dedication of the Tabernacle in their own way…No wonder those continual innovators, the rabbis, sought the cause of the priest’s deaths elsewhere. For while boundaries help create community, they can also keep communities from adapting and growing…This story warns us of the dangers of transgressing boundaries…

Judith Plaskow (Contemporary)