If the priesthood of Levi and Aaron, which provided the framework for the giving of the law, could really make people perfect, there wouldn’t have been need for a new priesthood like that of Melchizedek. But since it didn’t get the job done, there was a change of priesthood, which brought with it a radical new kind of law. There is no way of understanding this in terms of the old Levitical priesthood, which is why there is nothing in Jesus’ family tree connecting him with that priestly line.