It was specifically Aaron, not Moses, who merited the crown of the priesthood. The Sages explain that this is because of Moses’ earlier hesitation to accept the mission with which God tasked him when he was in Midyan. Despite this, Moses rejoiced in the joy of his brother and was not envious.

[After the seven days of inauguration, on the day of the dedication of the Tabernacle, the verse states:] “It was on the eighth day that Moses summoned Aaron and his sons, and the elders of Israel” (Leviticus 9:1). Our Sages said: On all seven days that Moses was at the burning bush, the Holy One, blessed be He, said to him: Go as My emissary. Moses said to Him: “Please send by means of whom You will send” (Exodus 4:13). So it was on the first and second days. The Holy One, blessed be He, said to Moses: I tell you: Go, and you say to Me: “Please send by means of whom You will send”? I take an oath by your life that in the future, I will repay you. When the Tabernacle will be built, you will believe that you will serve in the High Priesthood, but I will tell you: Call Aaron so that he can serve. Therefore, it is stated: “Moses summoned Aaron and his sons” (Leviticus 9:1). Moses said to Aaron: This is what the Holy One, blessed be He, told me: To appoint you as the High Priest. Aaron said to him: You exerted yourself in building the Tabernacle, and I will become the High Priest? Moses responded: I take an oath by your life that even though you are becoming the High Priest, it is as though I am being appointed. Just as you rejoiced with my ascent to greatness when I was chosen to lead the Israelites, I rejoice with your ascent to greatness. Why did Moses summon the elders of Israel? He did so in order to promote Aaron in the presence of the elders. The Holy One, blessed be He, said: Summon the elders and anoint Aaron, and I will confer greatness upon him in their presence, so they will not say: He became High Priest at his own initiative. (Tanĥuma, Shemini)