If perfection could have been attained through the Levitical priesthood—and indeed the law given to the people established that priesthood—why was there still need for another priest to come, one in the order of Melchizedek, not in the order of Aaron?
References for Hebrews 7:11
For when the priesthood is changed, the law must be changed also.
He of whom these things are said belonged to a different tribe, and no one from that tribe has ever served at the altar.
References for Hebrews 7:13
For it is clear that our Lord descended from Judah, and in regard to that tribe Moses said nothing about priests.
References for Hebrews 7:14