The full scope of Moses's argument against the angels is recorded in Shabbat 89a, and it is a masterclass in turning your opponent's own premises against them.
Moses went through the Ten Commandments one by one. "'You shall have no other gods before Me' (Exodus 20:3)—do you live among nations that worship idols?" The angels did not. "'Remember the Shabbat day to sanctify it' (Exodus 20:8)—do you do work that requires rest?" They did not. "'Do not take the name of the Lord your God in vain' (Exodus 20:7)—do you conduct business with each other that might lead to false oaths?" They did not.
"'Honor your father and mother' (Exodus 20:12)—do you have parents?" No. "'You shall not murder, you shall not commit adultery, you shall not steal' (Exodus 20:13)—is there jealousy among you? Is there an evil inclination within you?" No, and no.
The Torah was written for beings with bodies, families, desires, and flaws. Angels have none of these. The Torah was useless to them—and they knew it. They agreed with God that He was right to give it to human beings.
The verse that captures this reversal is (Psalms 8:10): "God our Lord, how glorious is Your name in all the earth"—but the phrase "Your majesty is placed above the heavens" no longer applies, because the angels themselves acknowledged that the Torah belongs below.
After their concession, every angel became an admirer of Moses and gave him a gift. Even the Angel of Death passed along a secret: that burning incense can halt a plague. When a pestilence struck Israel in the wilderness, Moses told Aaron to take the incense and stand between the living and the dead (Numbers 17:12–13). Without the Angel of Death's gift, Aaron would never have known the remedy.