Melchizedek was even greater than Abraham, and greater than Aaron and Levi by far. The Aaronic priesthood was not able to perfect us; a change of the law and priest was needed for that. God gave an oath with the second covenant; He didn't with the first. The first covenant required many priests, for they keep sinning dying; the new and better covenant only need the eternal Jesus.
Jesus' priesthood is based on a better covenant, which the first covenant itself taught us to look for in Jeremiah 31:31-34.
The first covenant taught us that access to the holy was still closed. Its earthly temple was just a copy of the heavenly presence, into which Christ entered with His own blood, and purified us once for all.
First covenant sacrifices didn't deal with sin, or they would have stopped. Jesus' sacrifice was a one-time deal, because it deals completely with sin. So approach God with boldness through Christ. If you violated the first covenant, the death penalty awaited you; how much worse if you violate the greater second covenant in Christ's blood? You have suffered mightily for Christ; don't shrink back now. You aren't of that sort; you will persevere in faith.