Chazal seek their sin, while seeking to reconcile the reason given in the Torah with the explanation. Rabbi Elazar says the two sons of Aharon died only because they issued a halachic ruling before Moshe, their teacher, while Rabbi Yishmael says it was because they entered the sanctuary intoxicated with wine. The Bartenura explains the meaning of Rabbi Elazar’s position – they issued a ruling that even though fire descends from heaven to consume the Korban, it was a Mitzvah for them to bring ordinary fire (ַקְרִיבוּ אֵשׁ זָרָה וַיָּבִיאוּ). But they sinned in this matter, as Hakadosh Baruch Hu had not commanded such – meaning, they should not have issued a ruling before Moshe, their teacher. This is derived from the redundancy of אֲשֶׁר לֹא צִוָּה אֹתָם, as it would have sufficed to write אֵשׁ זָרָה alone. Similarly, Rabbi Yishmael, who says they entered the sanctuary intoxicated with wine, means they offered a strange incense – i.e., they issued a ruling to bring ordinary fire before Moshe, their teacher, because they were intoxicated with wine. This is derived from the fact that after their death, the remaining ones were warned about the prohibition of drinking wine before performing entering the Mikdash. Rabbi Eliezer holds that this warning was given after their death to say: “Be careful in your service and do not enter intoxicated with wine, lest you err and issue a ruling before your teacher.”
The Siftei Chachamim asks a profound question. Following the death of Nadav and Avihu, the Torah says:
וַיְדַבֵּר מֹשֶׁה אֶל־אַהֲרֹן וְאֶל אֶלְעָזָר וְאֶל־אִיתָמָר בָּנָיו הַנּוֹתָרִים קְחוּ אֶת־הַמִּנְחָה הַנּוֹתֶרֶת מֵאִשֵּׁי ה' וְאִכְלוּהָ מַצּוֹת אֵצֶל הַמִּזְבֵּחַ כִּי קֹדֶשׁ קָדָשִׁים הִוא׃
And Moshe spoke to Aharon and to Elazar and Itamar, his remaining sons: Take the meal offering that remains from Hashem’s fire offerings and eat it as matzot beside the altar, for it is most holy.
Rashi says, הַנּוֹתָרִים means the remaining from death, teaching that even they were sentenced to death for Cheit Ha’Eigel, as it says וּבְאַהֲרֹן הִתְאַנַּף ה' מְאֹד לְהַשְׁמִידוֹ – And with Aharon, Hashem was very angry to destroy him, and “destruction” means the loss of children. Moshe’s Tefillah – וָאֶתְפַּלֵּל גַּם־בְּעַד אַהֲרֹן בָּעֵת הַהִוא – nullified half of this decree, however. The question arises though, if Moshe davened and, so to speak, halved the decree so that instead of four sons, only two died, why did Elazar and Itamar not die, when they were of a lower stature than Nadav and Avihu?
The Siftei Chachamim writes, if you bring the two additional reasons (in addition to Cheit Ha’Eigel) of our Tana’im – one saying it was because they issued a ruling before their teacher, and one saying it was because they entered the sanctuary intoxicated with wine – it can be said that both reasons contributed to the outcome. If it were only a settling of Cheit Ha’Eigel, why did Hakadosh Baruch Hu wait until now? Alternatively, why did He kill Nadav and Avihu and not Elazar and Itamar? Rather, there must be another sin, in addition to Cheit Ha’Eigel, according to each opinion. If it were only the latter reason, there’d be no punishment without a warning, so Cheit Ha’Eigel, which had a warning, is also necessary. Because Nadav and Avihu had sins of the strange fire and intoxication, they died, and not Elazar and Itamar.