This is from a pre-internet journal I used to keep.
The Se’ir Rosh Chodesh of Aharon. (5759-1999) Dr. Krinsky asked me, how is it possible that immediately after the death of Nadav and Avihu, which according to some was for paskening lifnei rabban, that Aharon burned the korbon of Rosh chodesh without asking Moshe! And you can’t answer that to Aharon it was even more poshut than bei’asah be’kutcha, because we see that Moshe didn’t realize that Aharon was right at first. So I told Dr. Krinsky that maybe Aharon wasn’t a talmid, or at least that he was a talmid chover. But then I turned to Moshe, who hadn’t heard the conversation, and asked him whether he thought that Aharon was considered a talmid of Moshe, or was he an equal. Moshe answered, “Aharon must have been an equal to Moshe, because if he wasn’t, he wouldn’t have burned the se’ir Rosh Chodesh without asking Moshe.” Dr. Krinsky couldn’t believe that Moshe hadn’t heard our conversation, but the fact is, he hadn’t.
(5760-2000). I checked the sforim, and it turns out that both Reb Moshe and the Lutzker Rov ask the question-- but the Lutzker Rov on 10:19 asks on Aharon, and so he says that Moshe and Aharon were ‘shkulim’, as above; Reb Moshe, on the other hand, asks the question on Elozor and Isomor (in the first Dorash Moshe, on 10:20,) and he answers that since Rashi says that Moshe admitted that he learned the drosho of Aharon from Hashem but forgot it, this shows that he had taught it to them, and so there was no halacha of moreh lifnei rabbonI asked the kids the question again this year, and both Mordechai and Ita showed me the Rashi in 10:19 that says that the reason Aharon answered Moshe, when Moshe had directed his question to Elozor and Isomor, was that it would not be appropriate for a talmid to respond to his rebbi’s tayneh. This, they said, shows that while Elozor and Isomor were considered Moshe’s talmidim, Aharon was not.
I also saw the Ohr Hachaim, who says that Aharon’s drosho from Maiser is so clear, that this din has a halacha of ‘bei’aso bekutcho.’
(August 2000/5760) I saw the Mishneh in Avos 4:12, and the Machzor Vitri’s pirush there, and the Avos D’rav Nosson towards the end of Perek 27 and the pirush of the Ben Avrohom there. The bottom line is, that almost everyone says that Moshe was the rebbi (obviously, and as the Gemora in Eruvin 54b says,) but since Aharon was older, they were considered ‘shkulim’. This doesn’t, however, affect the fact that Moshe was the Rebbi, and there should be a halocho of moreh lifnei rabbo. Also— the Medrash Rabba in Shemos 3:17 says, on “ve’atta tihiyeh lo leilohim”, that even though Aharon was older, since Moshe was the rebbi, Aharon had to be mechabed Moshe like he was mechabed the Shechina (moreh Rabboch kimoreh shomayim.)
(February ‘03/Adar I ‘63) I saw that the Netziv in the beginning of Parshas Tetzaveh (Shemos 27:20) says, after bringing several of the aforementioned rayos, that Aharon did not have a din of a talmid. Although he did learn from Moshe, after he learned from Moshe he did not need him, and he was considered an equal gadol. However, Moshe’s gadlus was in pilpul and chiddush, while Aharon’s was in svoro yeshoro and emes, ‘lehoros es Bnei Yisroel.’ And then he brings that this advantage of Aharon in svoro yeshoro resulted in Aharon’s ascension over Moshe when Aharon paskened correctly regarding the Se’ir Rosh Chodesh