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
And what we have said is even more clear if another priest like Melchizedek appears,
one who has become a priest not on the basis of a regulation as to his ancestry but on the basis of the power of an indestructible life.
For it is declared: “You are a priest forever, in the order of Melchizedek.”
References for Hebrews 7:17
The former regulation is set aside because it was weak and useless
References for Hebrews 7:18
(for the law made nothing perfect), and a better hope is introduced, by which we draw near to God.
References for Hebrews 7:19
And it was not without an oath! Others became priests without any oath,
but he became a priest with an oath when God said to him: “The Lord has sworn and will not change his mind: ‘You are a priest forever.’ ”
References for Hebrews 7:21
Because of this oath, Jesus has become the guarantor of a better covenant.
References for Hebrews 7:22
Now there have been many of those priests, since death prevented them from continuing in office;
but because Jesus lives forever, he has a permanent priesthood.
References for Hebrews 7:24
Therefore he is able to save completely those who come to God through him, because he always lives to intercede for them.
References for Hebrews 7:25