Parshas Tetzaveh is an anomaly in the Torah. It is the only parsha in the narrative of the Jews of that time in which Moshe Rabbeinu’s name does not appear at all, from his birth until the end of the Torah (barring certain parts of Devarim, where he was the person speaking).
The Ba’al HaTurim comments on the first pasuk in Tetzaveh (27:20) that in Parshas Ki Sisa, after seeing the Golden Calf and subsequently Hashem’s wrath through the plague, Moshe pleaded that “ וְעַתָּה אִם תִּשָּׂא חַטָּאתָם וְאִם אַיִן מְחֵנִי נָא מִסִּפְרְךָ אֲשֶׁר כָּתָבְתָּ – And now, if You forgive their sin But if not, erase me now from Your book, which You have written.” (32:32). The Ba’al HaTurim explains that although Hashem did indeed refrain from destroying the nation, a tzaddik’s word is always fulfilled.
The parsha in which Moshe’s name does not appear is about the kehuna, the priesthood, which was given to Ahron. R’ Yakov Minkus explains that there are 2 ways for Torah (representing Heaven) and mankind (representing Earth) to intersect:
1. The first way is that the Torah descends from Heaven. Moshe embodied this, as exemplified when he brought down the luchos from the mountain to the people.
2. The second is that we elevate become elevated ourselves. Ahron embodied this, as the ultimate “people’s person”. He was אוהב שלום ורודף שלום – a lover and pursuer of peace. The entire priesthood was based on helping the people interact with Hashem through the services.
The Gemara in Sanhedrin concludes that there are two ways to settle litigation, through din emes (an actual judgement), or a pshara (a compromise). The fact that both are valid settlements shows that both are equally powerful at achieving their goal, settling a dispute.
The role of the kohen is to play the arbiter, the middle man. As a man of the people, he is meant to feel their emotions, guide them through the services in the Beis HaMikdash, and follow the path that Ahron set.
If we are to say that this way of getting to the intersection of people and Torah is equally valid, Moshe almost had to be left out, to show that here is another, equally valid way.
There are various incidents in the Torah where Ahron and Moshe are mentioned, with Ahron preceding Moshe, as opposed to the usual Moshe first, and Ahron second. This is meant to show their equality. But as pointed out in many places, Moshe was the greatest man to have ever lived, without equal, so to what ends can we suggest their equality?
Knowing what we now know, the answer is simple. Their equality was not as people, as indeed Moshe was without equal, but rather, their equality was in the validity of their approaches in how to get the Torah to the people.