Why did Paul spend so much time discussing Melchizedek in Hebrews?

Paul's extended discussion of Melchizedek serves to reinforce the idea that Jesus' priesthood is superior to the Levitical order. By detailing Melchizedek's role as a priest who predates the law and who is without genealogy, Paul establishes that Christ's priesthood is eternal and not bound to the limitations of the old covenant. This significance is paramount to the Christian faith, demonstrating that Christ's one-time sacrifice is sufficient for all believers. Moreover, this comparison illuminates the transformational nature of Christ's work, as he fulfills what the law and previous priesthoods could not accomplish, thereby securing our redemption forever.