Hebrews 7: Jesus > Priests

In continuing to extol Jesus as superior in every way, the author of Hebrews goes to great lengths to demonstrate how Jesus surpasses and exceeds the Levitical priesthood.

His argument is that Jesus belongs to the priestly order of Melchizedek.  Here are the ways Jesus and Melchizedek are similar:

• Both receive tithes.
• Both are "kings of righteousness."
• Both are "kings of Salem" (Melchizedek's base "Salem" became "Jerusalem" - where Jesus was crucified.)
• Both have supernatural lineages (Melchizedek exists in scripture with no genealogy; Jesus likewise has a heritage that is otherworldly.)
• Neither Melchizedek nor Jesus are Levites.
• Melchizedek's priesthood is not described as ending, neither is Jesus' priesthood limited.

Another remarkable similarity that Hebrews does not mention: Melchizedek brought out gifts of "bread and wine" to Abraham - Jesus consecrated the elements of "bread and wine" to represent His body and blood.

Why does the author of Hebrews dwell on this?  He is making the point that Jesus' priesthood exceeds that of the Levitical priesthood in operation in the first century.  In other words, Christianity is superior to Judaism.  In a letter written to Hebrews specifically, the author is arguing the case for why Jews should look to Jesus as their Lord and Savior - He is the fulfillment of their faith in a way that Moses and Aaron can never be.