In the previous argument with Aaron about eating the sin-offering, why didn't Moses eat it himself, for he, unlike them, was not precluded by mourning? Rav answered - he was busy talking to God from morning till evening.
When Miriam contracted leprosy, it was not Moses, who was not a kohen, who pronounced her status, and not Aaron, who was a relative, but it was God himself, who also was a kohen, Who confined her and later released her. We see from this that Moses was not a kohen! - No, maybe leprosy is specifically given to the sons of Aaron to decide.
In truth this is an argument found between earlier authorities of the Mishna, for when God became angry with Moses for refusing to go Egypt, this, unlike all other angers, left no mark - so says Rabbi Yehoshua ben Korcha. However, Rabbi Shimon says that this anger too left a mark, and Aaron became a kohen instead of Moses, who thus remained a Levi.
Art: Jules Charles Boquet - Mourning