Correction: Jesus and Melchezedek are the ONLY members of the Melchizedek priesthood. Melchezedek was a foreshadow of Christ.
This is not an open party that everyone and anyone can come too. Contrary to some opinions.
There is no correction, when Peter tells us that we are an holy nation and a "royal priesthood", what order of priesthood (brotherhood of priests) do you think the members of the royal priesthood are under? The Aaronic priesthood, or the Melchisedec priesthood, or no priesthood? In lieu of the word "priesthood" being mentioned several times in the NT, it would be biblically illogical to say there was no priesthood.
So tell me, what priesthood does the "royal priesthood" refer to, the old Aaronic priesthood, or the new Melchisedec priesthood? It does seem obvious.
Jesus is the great High Priest of the Melchisedec priesthood. Does he not need helpers here on earth to accomplish the tasks that are done in the name of the Father and the Son and the HS, when he is in heaven?
Those tasks are accomplished by apostles, and prophets, and bishops, and elders, and pastors, and evangelists, and teachers, and priests (different duties than the Aaronic priests), and deacons. The priesthood having been changed from the priesthood of Aaron to the priesthood of Melchisedec would absolutely look different, hence new covenant, new offices of the priesthood, etc., etc.
The main difference is that the Melchisedec priesthood was expanded from just 1 family tribe (Levites) to all worthy male members of the church, from all the nations of the earth.
The concept that Jesus and Melchisedec are the only members of the Melchisedec priesthood was started by some guy that was trying to argue that the priesthood even exists.
The concept that Jesus and Melchisedec are the only 2 people in the history of the world that are qualified to hold the Meichisedec priesthood was made up by some guy that was trying to figure out how he could deny the priesthood exists.
He got it wrong, and has driven billions of people to know nothing of the Melchisedec priesthood, which is the "royal priesthood" mentioned by Peter in the bible. It is royal because it is the priesthood of our King, Jesus Christ, who is the great High Priest of our priesthood.