Since the request was given in Parshas Ki Sisa, next week, this parsha is the last occasion prior to the next reading of the request for it to be honored. This shows Hashem's reluctance to actually remove Moshe from the narrative.However, there are other reasons for doing so. Rabbi Sorotzkin points out that this parsha is the one that is always read during the week of Moshe's birthday and yahrtzeit (death anniversary) and as such contrasts with the situation in "other religions" which connect all their observances and holidays to the founder's life and death. Instead, the very lack of a celebration or mention of Moshe's name at this time shows that the important events are those of the Torah and the establishment of service of Hashem.
Another point is that it shows the humility of Moshe Rabbeinu in that he joyfully withdrew to allow his brother, Aharon, to be fully recognized as the Kohen Gadol and acknowledge his full authority over the spiritual realm. Indeed, Rabbi Sacks points out that this is a necessary occurrence for there to be a valid and lasting society. As he says in this week's Covenant and Conversation
Thus, it is a necessary factor for the existence of the nation of Israel.
I could bring up the modern politicians who have shown the reverse trait so that we know what problems that they have caused. This is true not only in the United States, but also in the State of Israel. I will not mention specific names but we all know who they are and what they have done.Moses must show the people – and Aaron himself – that he has the humility, the tzimtzum, the power of self-effacement, needed to make space for someone else to share in the leadership of the people, someone whose strengths are not yours, whose role is different from yours, someone who may be more popular, closer to the people, than you are – as in fact Aaron turned out to be.Lehavdil: in 2005 the historian Doris Kearns Goodwin published an influential book about Abraham Lincoln entitled Team of Rivals. In it she tells the story of how Lincoln appointed to his cabinet the three men who had opposed him as candidate for the Republican party leadership. William Henry Seward, who had been expected to win, eventually said of him that “his magnanimity is almost superhuman . . . the President is the best of us.” It takes a special kind of character to make space for those whom one is entitled to see as rivals. Early on, Aaron showed that character in relation to Moses, and now Moses is called on to show it to Aaron.True leadership involves humility and magnanimity. The smaller the ego, the greater the leader. That’s what Moses showed in the parsha that does not mention his name.
Another point can connect this parsha with Parshas Zachor. Just as we must erase the memory of Amalek, we also "erase" the memory of Moshe Rabbeinu who fought Amalek. Just as the Mishkan was created as a communal effort, so too is the fight against Amalek a communal effort. Thus, we do not "remember" the individual who gave us the basis for the mishkan but we show it as a full communal effort. with the Kohanim becoming the representatives of the people. The bigdei kehunah show this status. The Kohen Gadol is not specifically Aharon but whoever is in that office will show the greatness that Hashem has assigned to the office. Just as Aharon took over the office from Moshe, so too will each of his successors take over the office and be responsible for the generation in which he serves.