Miriam and Aaron criticized Moses. The Hebrew Bible is vague about why. The Targum Jonathan fills in the backstory with a Cushite queen, a celibate prophet, and a divine rebuke that equated leprosy with death.
The Targum says Miriam and Aaron spoke against Moses regarding "the Kushaitha whom the Kushaee had caused Moses to take when he had fled from Pharaoh." This refers to a tradition that Moses became king of Cush (Ethiopia) during his years in exile and married the Cushite queen—but then "sent her away." Their complaint was not about the marriage itself but about its implications: "Moses separated himself from married life." They argued: "Has the Lord spoken only with Moses? He has spoken with us too, and we have not separated from our spouses."
The Targum describes Moses as "more bowed down in his mind than all the children of men upon the face of the earth"—rendering the Hebrew word anav (humble) as psychological lowliness, not mere modesty.
God's response to Miriam and Aaron distinguished levels of prophecy. Other prophets received revelation "in apparition, speaking with them in a dream." But Moses: "Speaker with speaker have I spoken with him." God revealed Himself to Moses "at the bush" and Moses "beheld the likeness of My Shekinah (the Divine Presence)." No other prophet saw that.
Miriam was struck with leprosy. Aaron begged Moses for mercy, comparing Miriam to a baby who dies at birth after completing full term in the womb. He pleaded: "She was with us in Egypt, seeing our captivity, our dispersion, our servitude; but now, when the time has come for our going forth to possess the land, she is kept back from us."
God agreed to limit her punishment to seven days, adding: "If her father had corrected her, would she not have been disgraced seven days? But today, when I correct her, much more right is it that she should be dishonored fourteen days." The Targum then explains that because Miriam once watched over baby Moses at the Nile for a small hour (Exodus 2), the entire nation—600,000 people, the Cloud of Glory, the Tabernacle, and the miraculous well—all waited for her healing.