Numbers 12:1-15 records the rebellion of Miriam, who was Moses' older sister. Moses was the God-chosen leader, and Miriam was a prophetess who, after the crossing of the Red Sea, led the women in praising God (Exo. 15:20-21). Although she was Moses' sister and served together with him, she still rebelled against him. This indicates that even those who are very close to one who takes the lead among God's people may rebel against him.
Miriam rebelled because she was jealous of Moses' position in the oracle of God. She, along with Aaron, said, "Has Jehovah indeed spoken only through Moses? Has He not spoken through us also?" (Num. 12:2).
Miriam took as a cloak for her rebellion the weakness of Moses in marrying a Cushite woman (v. 1). I do not know why Moses did this or when he did it. Perhaps this was a weak point in Moses' life, but this weakness did not spoil his function. Miriam used this weakness as an excuse, as a standing, to rebel against Moses.
God came in to deal with Miriam's rebellion. She was condemned by God and suffered the punishment of leprosy (vv. 6-15a), a disease which indicates that one's sickness is inward. Suffering such a punishment, Miriam was shut up outside the camp for seven days.
As a result of Miriam's rebellion and punishment, the journey of the people was delayed for seven days (v. 15). Her rebellion surely was a frustration to God's people.