Jesus as Human and Divine Priest
There are three passages in Hebrews that are critical to the concept of Jesus as a priest who combines divine and human attributes.
17For this reason it was necessary for him to be like his brethren in all ways, so that he could become a merciful and faithful high priest concerning divine matters {matters dealing with God} in order to cleanse the sins of the people. 18Because he was tested by the things he suffered, he is able to sympathize with those who are tested. — Hebrews 2:17-18 (TFBV project)
14Since we have such a great high priest who has passed through the heavens, Jesus the son of God, let us grasp our confession. 15For we do not have a high priest who is unable to sympathize with our weaknesses, since he has been tested in all things in the same way we have, but without sin. 16Let us approach the throne of grace with confidence, so that we might receive mercy and we might find grace in time of need. — Hebrews 4:14-16 (TFBV project)
These two talk mostly about the human attributes, though they hint also at the divine. The next one purely describes the divine attributes:
26We now have just such a suitable high priest, holy, blameless, undefiled, separated from sinners and come to the highest places of the heavens. 27He has no need to offer sacrifices each day first for his own sins, like the other high priests and then for those of the people, because he has offered himself once and for all. 28For the law appointed high priests who had weaknesses, but the word confirmed with an oath, which came after the law, appointed a Son, perfected forever. — Hebrews 7:26-28 (TFBV project)
Recall that this is all being written well before the formulation of the doctrinal creeds in which the Christian community declared Jesus fully God and yet fully human. Without such a doctrinal explanation, however, we have here both elements of that doctrine. In the first passage, Jesus is our brother, one of us, having suffered temptation and faced death as we must do so, but always with the emphasis on the fact that he did not sin. Our second passage (Hebrews 4:14-16) introduces the heavenly side of the priest, but is still primarily concerned with sympathy for our weaknesses. The emphasis is on what he shares with us.
In Hebrews 7:26-28, the emphasis has shifted completely. Jesus is able to sacrifice properly for us because he does not need to sacrifice for himself, being without sin. He is set apart from us, holy, so he can approach God. But then there is that other aspect; because he is our brother, he can also invite us to approach God with equal boldness. The approach to the throne of grace is made possible by the divine-human combination in the new high priest.
Let’s tie this in as well to the interpretation of Hebrews 6:4-6. There we have a dire warning of destruction for anyone who falls away. But that warning can only be heard in the light of this encouragement. God, presented to us in the person of Jesus, is able to sympathize with our weaknesses, because he has seen them in action and suffered their testing. The intended message is one of great hope but yet serious warning. The author of Hebrews believes we will never get a better invitation than this.