6: As he saith also in another place, Thou art a priest for ever after the order of Melchisedec. 7: Who in the days of his flesh, when he had offered up prayers and supplications with strong crying and tears unto him that was able to save him from death, and was heard in that he feared; 8: Though he were a Son, yet learned he obedience by the things which he suffered; 9: And being made perfect, he became the author of eternal salvation unto all them that obey him; 10: Called of God an high priest after the order of Melchisedec. 11: Of whom we have many things to say, and hard to be uttered, seeing ye are dull of hearing. 12: For when for the time ye ought to be teachers, ye have need that one teach you again which be the first principles of the oracles of God; and are become such as have need of milk, and not of strong meat. 13: For every one that useth milk is unskillful in the word of righteousness: for he is a babe. 14: But strong meat belongeth to them that are of full age, even those who by reason of use have their senses exercised to discern both good and evil.
There is no actual priesthood of Melchisedec except in the sense that Melchisedec was himself. Christ has a priesthood that has some similar features and this is what the writer to Hebrews is saying. There is no record in scripture of the birth or death of Melchisedec and Christ’s ministry is like that he is an eternal person and so therefore unlike the Aaronic priests who died and their ministry ended Christ’s ministry goes on eternally. Christ’s ministry of prayer for Israel is described here as - prayers and supplications with strong crying and tears. Christ as a son and as a man learned obedience through his suffering. We see this in the garden where he sweated great drops of blood as he contemplated the suffering to come. And his obedience was fully completed, that it was made perfect and he became ‘the author of eternal salvation unto all them that obey him’. The writer to the Hebrews confesses that there is much more that he could say but that they would not understand. He says at this stage you should be the teachers of these things yet you are still struggling to understand the alphabet. He says you are babies in understanding. Those that are mature have the ability to make difficult decisions regarding moral issues.