11 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.
15 But the Melchizedek story provides a perfect analogy: Jesus, a priest like Melchizedek, not by genealogical descent but by the sheer force of resurrection life - he lives! - "priest forever in the royal order of Melchizedek." The former way of doing things, a system of commandments that never worked out the way it was supposed to, was set aside; the law brought nothing to maturity. Another way - Jesus! - a way that does work, that brings us right into the presence of God, is put in its place.
20
The old priesthood of Aaron perpetuated itself automatically, father to son, without explicit confirmation by God. But then God intervened and called this new, permanent priesthood into being with an added promise:
God gave his word;
he won't take it back:
"You're the permanent priest."
This makes Jesus the guarantee of a far better way between us and God - one that really works! A new covenant.
23 Earlier there were a lot of priests, for they died and had to be replaced. But Jesus' priesthood is permanent. He's there from now to eternity to save everyone who comes to God through him, always on the job to speak up for them.
26 So now we have a high priest who perfectly fits our needs: completely holy, uncompromised by sin, with authority extending as high as God's presence in heaven itself. Unlike the other high priests, he doesn't have to offer sacrifices for his own sins every day before he can get around to us and our sins. He's done it, once and for all: offered up himself as the sacrifice. The law appoints as high priests men who are never able to get the job done right. But this intervening command of God, which came later, appoints the Son, who is absolutely, eternally perfect.