Hebrews reminds me so much of the Gospel of Luke and the book of Acts – not in content, but in form. The writer of all these books has a habit of introducing a subject, then leaving it and returning to it as he expands and integrates that subject with the larger theme of his book.
Melchizedek is mentioned only twice in the Old Testament. But the writer of Hebrews makes much ado of him in this book.
The writer introduces us to the idea of Jesus as a high priest in chapter 2. In chapter five, he tells us Christ’s priesthood is not of the Levitical order, but of the “order of Melchizedek..” He draws this conclusion from Psalm 110, a Psalm used numerous times in the New Testament (by Jesus) to refer to Jesus (cf. Matthew 22:44 and parallels). Peter uses it the same way in his Pentecost sermon (Acts 2:34-35). In chapter seven of Hebrews, the writer explains why it is so important. Melchizedek was a member of a greater priesthood than that of Levi since even Abraham paid him tithes and was blessed by him (the lesser is blessed by the greater). Playing off the mysteriousness of the Melchizedek priesthood (we don’t know anything about the guy – where he came from or where he went), the writer of Hebrews proclaims it an eternal priesthood. The fact that God promised (during the days of the Levites in Psalm 110) that a priest was coming who would be of this order signifies the limited usefulness of the Levites. The fact that Jesus, whose priesthood is of this order, lives forever makes not only his “order,” but his service as a high priest greater than all other high priests. He is always there for us.
To a group of Christians considering abandoning their faith, the unstated question is inescapable: if you abandon Jesus, where will you turn. Whatever you turn to will be inferior in every way.
I don’t want to leave this without making an important point: You should not think that the writer of Hebrews thinks his readers are going to abandon Church for Synagogue. The issue is not competing religions. As the book comes to a close, we will see their abandonment of Jesus is not so much a matter of switching doctrinal orthodoxy as it is abandoning the behavior in daily life Jesus requires. Once they leave the life of Jesus for the way of the world, there is no hope left. That was the point of Hebrews chapter six.