Another reason that Christ is a greater high priest is because His sacrifice is able to deal with sins once for all.
The writer of Hebrews makes the case that the religious observances of the OT were not sufficient to take away sins, but the sacrifice of Jesus is.
Because of this new covenant that Jesus has initiated, mere humans can have an personal and intimate relationship with Almighty God.
Because Christ is our great High Priest, He is able to save to the uttermost all who call upon Him.
The writer of Hebrews gives an explanation of who Melchizedek is, thus pointing to God's greatness and sovereignty in orchestrating this even in Abraham's life.
The reason we can trust God is because of the certainty of His promises that he has guaranteed through Himself.
The writer of Hebrews exhorts his readers to stop remaining immature in their faith and to grow in their relationship with God.
The difference between the priesthood of Aaron and the priesthood of Christ is His sinlessness, whereby He is able to intercede on our behalf.
Because we have a great High Priest, we can come boldly to the throne of grace to find help in our time of need.
The writer of Hebrews uses the example of the Israelites to show how easy it is to harden our hearts and the necessity of keeping our hearts soft before God.