“He is without father or mother or genealogy, having neither beginning of days nor end of life, but resembling the Son of God, he continues a priest forever.”
First of all, this verse is not to be construed as a literal commentary of the physical life of the person known as Melchizedek. People who set off to do this miss the meaning of the writer who is not interested in anything about Melchizedek except his role as king and priest and its relationship with Jesus in the same capacity.
There are three priesthoods under consideration in this section of the book. Basically, the writer wants to compare the Levitical-Aaronic priesthood with that of Jesus. He does that by comparing the Levitical one with the Melchizedek. This gives the historical basis of a non-Levitical priesthood. Jesus was not a Levite, and neither was Melchizedek. Therefore the priesthood of Jesus was modeled on Melchizedek’s.
Melchizedek has no genealogical background to be a priest. No one in his family, past or future, served as priests. Yet, it is plain that God accepted him as such, allowing Abraham to pay tithes to him. Jesus has no family connections to the priesthood as far as His physical life is concerned. Spiritually, all of His children will become priests by virtue of being adopted into His family. In reality, Melchizedek is a priest like Jesus rather than the other way around.
Task for Today: If you are a child of the Most High, you become a priest in the line of Jesus. You do have the correct genealogy to serve as a priest. Are you serving? Do you minister in the kingdom?