After The Order of Melchizedek

The Melchizedek priesthood shows that Jesus wasn't a priest based off genealogy

The reason that Melchizedek was without mother, father or genealogy was because the Bible doesn't talk about his father, mother or genealogy, not because he doesn't have any of those things. It says that he was a priest forever because the Bible doesn't discuss his death either, so it's a mystery, which made him similar to Christ. Christ is a priest based off the similitude of Melchizedek, but Christ being the true form.

Melchizedek:

1. Was not Christ, but the priesthood was after the order of, meaning the similitude of Melchizedek

2. Was not a celestial being, but a man

3. Just like Joseph was a type of Christ, Melchizedek was a type of Christ, but Christ is the real deal.

Melchizedek was a "type" of Christ:

1. King of righteousness and peace (Romans 3-5:1; 14:17; Isaiah 32:17, Colossians 1:30, Joshua 10:1-3)

Hebrews 7:11-19 (David predicted that the Melchizedek priesthood would replace the Levitical priesthood)

Hebrews 7-10 (the development of the ultimate priesthood)

Hebrews 5:12-14 (was the very material too strong to nourish babes)

Melchizedek priesthood:

Revelation 1:19

1. Write the things which thou hast seen (the vision of Christ, chapter 1)

2. And the things which are (the 7 churches, chapters 2 & 3)

3. And the things that shall be hereafter (which follows after the churches, chapters 4-22)

Melchizedek priesthood:

Jesus Christ (the lion in Jacob's final blessing to his sons: Genesis 49:8-10; Hosea 5:14; Hebrews 7:14)

Jesus Christ (root of David in Isaiah 11:1&10; Jeremiah 23:5-6; Romans 15:12; Revelation 22:16; Matthew 1:1)

Jesus Christ (he’s the result of David's line, yet he was the one who brought David and the line into existence; he used this paradox to baffle the Pharisees in Matthew 22:41-46)(in God's covenant with David, his line was to rule over all the whole earth in 2 Samuel 7 and Psalm 2:8 which was confirmed to Mary in Luke 1:33)

Christ being a priest after the order of Melchizedek just showed that

Christ priesthood was greater than Levitical priesthood (Hebrews 7:1)

Melchizedek offered bread and wine (1 Corinthians 11:26)

It's not Melchizedek's priesthood, but it's in the similitude of Melchizedek's priesthood, that's what it means when it says order. Plain English, it's similar. 

The book of Hebrews shows:

1. A God-man better than the angels

2. An apostle better than Moses

3. A leader better than Joshua

4. A priest better than Aaron

It shows:

1. Jesus has a better position,

2. Jesus is a better priest

3. The new priesthood is based on a better covenant

4. The new priesthood functions in a better sanctuary

5. The new priesthood is based on a better sacrifice