Most attention paid to Parashat Shemini focuses on the divine fire that consumed Nadav and Avihu when they tried to offer a strange fire on the brand new altar at its triumphant moment of inauguration (VaYikra 10:1-2).  No fewer than twelve explanations  are offered in Rabbinic literature to explain why God took their lives.
However, it seems worthwhile to me to focus more on the aftermath of this shocking event.  After Moshe’s bizarre poetic eulogy (v. 3), after the immediate removal of the corpses (vv. 4-5), after Moshe’s rapid-fire, sober instructions to the kohanim for the immediacy and for the generations (vv. 6-15), Moshe returns to check in on the other business of the day:  what is the state of the goat that had already been offered as the national sin ?  The mood may have gone haywire after Aharon’s sons were killed in the line of duty, but Moshe played it cool, unswayed by his nephews’ death, mind still on the urgent business of the day of managing God’s housewarming party.  Let’s take a look:

VaYikra 10:16-20:
“And Moshe urgently inquired about the goat of the sin-offering, and, behold, it was burnt!  And he raged against Elazar and against Itamar, the remaining sons of Aharon, saying: וְאֵת שְׂעִיר הַחַטָּאת דָּרֹשׁ דָּרַשׁ מֹשֶׁה וְהִנֵּה שֹׂרָף וַיִּקְצֹף עַל אֶלְעָזָר וְעַל אִיתָמָר בְּנֵי אַהֲרֹן הַנּוֹתָרִם לֵאמֹר.
‘Why have you not eaten the sin-offering in the place of the sanctuary, for it is the sacred of the sacred, and it was given to you by God to bear the iniquity of the congregation, to make atonement for them before YHWH?! מַדּוּעַ לֹא אֲכַלְתֶּם אֶת הַחַטָּאת בִּמְקוֹם הַקֹּדֶשׁ כִּי קֹדֶשׁ קָדָשִׁים הִוא וְאֹתָהּ נָתַן לָכֶם לָשֵׂאת אֶת עֲו‍ֹן הָעֵדָה לְכַפֵּר עֲלֵיהֶם לִפְנֵי יְהוָה.
Look, its blood was not brought inside, into the sanctuary; you were certainly supposed to have eaten it in the sanctuary, as I commanded!’ הֵן לֹא הוּבָא אֶת דָּמָהּ אֶל הַקֹּדֶשׁ פְּנִימָה אָכוֹל תֹּאכְלוּ אֹתָהּ בַּקֹּדֶשׁ כַּאֲשֶׁר צִוֵּיתִי.
And Aharon spoke unto Moses: ‘Look, today, had they offered their sin-offering and their burnt-offering before the YHWH, when all this has happened to me, and if I had eaten the sin-offering today, would it have been good in YHWH’s eyes?! וַיְדַבֵּר אַהֲרֹן אֶל מֹשֶׁה הֵן הַיּוֹם הִקְרִיבוּ אֶת חַטָּאתָם וְאֶת עֹלָתָם לִפְנֵי יְהוָה וַתִּקְרֶאנָה אֹתִי כָּאֵלֶּה וְאָכַלְתִּי חַטָּאת הַיּוֹם הַיִּיטַב בְּעֵינֵי יְהוָה.
And Moshe heard, and it was good in his eyes.” וַיִּשְׁמַע מֹשֶׁה וַיִּיטַב בְּעֵינָיו.

What’s going on in this passage?  Up until now, Aharon has been completely silent in the wake of his sons’ death, as the text emphasizes after Moshe’s ambiguous eulogy, adding, simply, “And Aharon was silent — וידם אהרן” (ibid., 10:3).  So the fact of Aharon speaking here is important, even as his point may be elusive.  What is he saying?  How and why do his words move Moshe?  What’s their dispute about?
Moshe attacked Aharon and sons on a point of halakhah, reminding them of the rule that the kohen must eat part of the sin-offering.  That’s exactly how the symbolic coherence of the sacrifice functions.  In his magisterial work on VaYikra, the late Prof. Jacob Milgrom explains that the sin-offering (hatat, possibly better rendered as “purification offering”) responds to a situation of impurity caused by sin, unstable health, or what-have-you.  The Kohen embodies sanctity/kedusha, which stands for life; while the carcass of the sin-offering embodies impurity, which stands for death. “When the priest consumes the [hatat] he is making a profound theological statement:  holiness has swallowed impurity; life can defeat death” (Anchor Bible Leviticus 1:16:  A New Translation with Introduction and Commentary, p. 639).  A lot is at stake in the proper consumption of the sacrifice.  If it is entirely burned on the altar, should Israel understand that death, chaos, and instability are triumphant forces?
This symbolic logic was central to the grammar of the Israelite rite, but it was not culturally self-evident.  “Now it has been shown that in the ancient Near East, ritual detergents were always destroyed after they were used lest their potent remains be exploited for purposes of black magic….By requiring that the [hatat] be eaten, Israel’s priests were able to affirm that the power to purge the sanctuary does not inhere in a ritual but is solely dependent on the will of God.  Moreover, they backed up their conviction by their act:  they ate the [hatat] and were willing to suffer the consequences if their conviction proved wrong” (637).
Let’s listen again to Aharon’s response:  “‘Look, today, had they offered their sin-offering and their burnt-offering before the YHWH, when all this has happened to me, and if I had eaten the sin-offering today, would it have been good in YHWH’s eyes?!”
Now, there are situations where the Torah stipulates that the sin-offering should be burned entirely:  1) if the High Kohen sins, endangering himself and the whole people (4:3-21); 2) if the entire people of Israel collectively sins in error (ibid.); 3) the annual sin-offering on Yom Kippur to purge the sanctuary on behalf of the entire people (16:27).   It’s in those extreme situations that the kohen does not have the capacity to embody sanctity and life to the degree necessary to overcome that magnitude of rupture and death; there, only God can consume the impurity embodied by the animal and thereby affirm the victory of life over death.
Aharon is correcting Moshe on a point of halakhah.  This case is like those.  A kohen in the throes of shocked encounter with death cannot successfully model the triumph of life over death any more than a kohen who brought sin upon the whole people can himself model stability and order prevailing over the disruption of sin.  Indeed, in the Talmud, tractate Moed Qatan,  several laws governing mourners in the liminal period between death and burial are learned from this story:  the Sages understood that this dialogue was a debate in halakhah.
What leads to a dispute like this?  Why did Moshe and Aharon see this case in such different ways?  The fact that each one is incredulous that the other doesn’t see it his way suggests that the difference between them is not just a question of interpretive judgment call, but in the fundamental framing of the task at hand.
What are mitzvot?  On the face of it, they are the enumeration of God’s will for the Jewish people in the world.  All that we need to know is there, as the mishna teaches, “Turn it over and turn it over, for all is in it” (Pirkei Avot 5:22).  The  Torah already told us a rule – the kohen eats the sin-offering — and enumerated the three exceptions.  The Torah is clear;  we have all the information.  “Moshe received Torah at Sinai” (Pirkei Avot 1:1).  His job is to teach its details to his people, to detail for them information that they do not know, to instruct them in the set rules of the chess game, as it were, as a humble recipient of a divine gift and public servant.  Through such an orientation, it is easy to see that Aharon and his sons apparently were required to eat the sacrifice and that they sinned egregiously and recklessly, preventing the people from achieving atonement.
But there is another orientation.   The enumerated mitzvot are first-tier examples, necessarily fragmentary, of the limitless fulfillment of God’s will.  Since God’s will is eternal and language is always bounded and shaped by context, it is impossible for everything to be enumerated, for every situation to be anticipated in a predictive list.  The Maggid Mishneh captured this in a famous comment on the Rambam’s code, in reference to the Torah’s broad commandment, “and you shall do what is right and what is good in the eyes of YHWH” (Devarim 6:18):  “And it would not have been appropriate in all this to command details, because the Torah’s commandments are for all ages and all times and every matter…while human traits and behavior vary according to time and personality, so the Sages, z”l, wrote some useful details falling under these general categories…” (Hil. Shekheinim 14:5).  The commandments are eternal, but our capturing of the application of the commandments cannot but be conventions and assessments for how to apply those eternal commandments to the local situation at hand.  If we are meticulous and attentive, they will hopefully be truly excellent and wise, reasoned and tested conventions“Turn it over and turn it over, for all is in it”:  turn it over and over, look at it from all possible angles and perspectives, and according to every consequence you can imagine.  It is then and only then that “all is in it”.  Torah ceases to be God’s eternal word the moment it is grasped as a list of static, finite, quantifiable, and complete statements.  There is no escaping human evaluation and decision-making.

“And Aharon spoke unto Moses: ‘Look, today, had they offered their sin-offering and their burnt-offering before the YHWH, when all this has happened to me, and if I had eaten the sin-offering today, would it have been good in YHWH’s eyes?! And Moshe heard, and it was good in his eyes.”  Aharon recognize that this case is not predicted by the Torah laws, and that that does not necessarily mean that it follows the general rule. This case resembles the thrust of the exceptions to the rule, which pointed the way toward interpretation.  Aharon made a judgment call and Moshe had the magnanimity to recognize Aharon’s insight and shift his own approach.

The Sages emphasize (Talmud Bavli Qiddushin 30a) that the exact middle of the Torah, is between the words darosh/darash, the emphatic, doubled verb of Moshe’s investigation of the sacrifice, the verb that comes to embody the core practice of Rabbinic life — midrash — as if to say that the crux of the Torah is right here in the interaction between Moshe and Aharon.  That the Torah hinges on the tension between the clear and emphatic, but mistaken, perspective of Moshe, the ambiguous and halting, but correct response of Aharon, and the acknowledgement by Moshe of Aharon’s way.  A mitzvah can be a mitzvah only when its potency is not domesticated to one snapshot of its translation.  Mitzvot are divine only when translated into human idiom that knows itself as such, by practitioners nimble enough to continue to unfold their potential, and when met with the human conviction to stand up for their myriad meanings and implications, even when they seem new or surprising.
Aharon’s message — the crux of the Torah — is that it is not actually safer or more conservative to hew to a conventional understanding of halakhah, overwhelmed by formal precedent.  That is just privileging one potential, local human application over another.  The more conventional read, self-consciously not creative, may be innovating a radical new meaning which does terrible damage to the mitzvah’s intent, just as eating the sin offering right after Nadav and Avihu’s death would have made a mockery and farce out of the eternal, Torah value of life consuming death, just at the moment when its correct understanding was most in need of enforcement.  The more surprising read, self-consciously interpretive, may also be grievously wrong, but it stands a better chance, because it knows what it is doing and to be cautious and vigilant in consideration of consequences.  The axis on which the Torah rests is the charge of Rabbinic responsibility:  midrash must be vigilant, ongoing, careful, focused on consequences, and practiced with conviction that no adjudication can avoid personal evaluation and the conviction to stick with it even if its results are unexpected.