There are ways in which Melchizedek was like God's Son.
Hebrews 7:1-3
Now I will say more about this man Melchizedek. He was the king of Salem city and was a priest of God, the one who is greater than anyone else. He met Abraham who was returning home after he and his men had defeated the armies of four kings [SYN]. Melchizedek asked God to bless Abraham. Then Abraham gave to him one tenth of all the spoils he took after winning the battle. Melchizedek's name means firstly ❛king who rules righteously❜, and since Salem means ❛peace❜, he was the ❛king who rules peacefully❜. In the Scriptures there is no record of who his father was, nor is there any record of who his mother was, nor is there any record of who his ancestors were. There is no record of when he was born, nor is there any record of when he died. For these reasons, it is as though he continues to be a priest forever, and for this reason he is like God's Son.
Melchizedek was greater than Abraham.
Hebrews 7:4-10
You can realize how great this man Melchizedek was from the fact that Abraham, our famous ancestor, gave him ◄a tithe/one tenth► of the spoils from the battle. According to the laws God gave Moses, the descendants of Abraham's great-grandson Levi, who were priests, should take tithes from God's people who were their relatives, even though those people also were Abraham's descendants. But this man Melchizedek, who was not among the descendants of Levi, took tithes from Abraham. He also asked God to bless Abraham, the man to whom God promised many descendants. We know for certain that it is the more important people who ask God to bless the less important people. And Melchizedek blessed Abraham. So we conclude that Melchizedek was greater than Abraham. In the case of the priests who are descendants of Levi, men who some day will die receive tithes. But in the case of Melchizedek it is as if God testifies that he was still living, since there is no record in Scriptures about his death. And it was as though Levi himself, and all the priests descended from him —who received tithes from the people —paid tithes to Melchizedek. And when Abraham paid tithes, it was as though Levi and all the priests descended from him acknowledged that the work Melchizedek did as a priest was greater than the work Levi did, 10 since the sperm from which all those priests were eventually born was still in Abraham's body [EUP] when Melchizedek met Abraham.
The former Jewish priests were not adequate, so a new one like Melchizedek had to come.
Hebrews 7:11-19
11  God gave his laws to his people at the same time he gave regulations about the priests. So, if what the priests who were descended from Levi did could have provided a way for God to completely forgive people for disobeying those laws, certainly no other priest like Melchizedek would have been necessary. [RHQ] Instead, priests who were descended from Aaron, Levi's descendant, would have been adequate. 12  But we know they were not adequate, because a new type of priest like Melchizedek has come. And since God has appointed a new type of priest, he also had to change the regulations concerning how priests were appointed { he appointed priests}. 13  Jesus, the one about whom I am saying these things, is a descendant of someone else, not a descendant of Levi. None of the men from whom Jesus descended ever served as priests [MTY]. 14  We know that since it is obvious that it is from the tribe of Judah that our Lord was descended. Moses never said that any of Judah's descendants would become priests. 15 Furthermore, we know that the priests who were descended from Levi were inadequate, since it is even more obvious that another priest has appeared who is like Melchizedek. 16 Jesus became a priest, but not because he fulfilled what God's law required about being a descendant of Levi. Instead, he has the kind of power that came from a life that nothing can destroy (OR, enabled him to live again after he was killed). 17  We know this since God confirmed it in the Scripture passage in which he said to his Son,
You (sg) are a priest eternally just like Melchizedek was a priest.
18 On the one hand, God canceled what he commanded previously concerning the priests because it failed in every way to enable anyone to become all that God intended. 19 Remember that no one was able to become all that God intended by obeying the laws that God gave Moses. On the other hand, God caused that we could confidently expect better things than we could expect by obeying God's laws. He did that by his establishing Christ as priest. Now by means of Christ sacrificing himself for us we can come near to God.
Jesus lives eternally as a Supreme Priest to plead with God for us.
Hebrews 7:20-25
20 Furthermore, when God appointed Christ, it was when God solemnly declared that Christ would be a priest [LIT]. When God appointed former priests, it was not by his solemnly declaring that they would be priests. 21 However, when he appointed Christ to be a priest, it was by these words that the Psalmist wrote in Scripture:
The Lord has solemnly declared to the Messiah,
—and he will not change his mind—
“You will be a priest forever!”
22 Because of that, Jesus guarantees that the new covenant will be better than the old one.
23 And formerly, the priests could not keep serving as priests, because they all died [PRS]. So there were many priests to take the place of the ones who died. 24 But because Jesus lives eternally, he will continue to be a Supreme Priest forever. 25 So, he can completely and eternally save those who come to God by trusting in what Jesus has done for them, since he lives forever to plead with God to help them.
Jesus is the kind of Supreme Priest we need, because he was sinless.
Hebrews 7:26-28
26 Jesus is the kind of Supreme Priest that we need. He was holy; he did no wrong; he was completely innocent. God has now taken him up to the highest heaven separated from living among sinners. 27  The other Supreme Priests need to sacrifice animals day by day as well as year by year. They do this, firstly, to atone for their own sins, and then to atone for other people who have sinned. But because Jesus never sinned, he does not need to atone for his own sin. The only thing he needed to do to save people was to sacrifice himself once! 28  We need a Supreme Priest like him, because in the laws that God gave Moses [PRS] the ones who would be appointed to be priests would be men who tended to sin easily. But God solemnly declared [PRS] after he had given his laws to Moses that he would appoint ◄his Son/the man who is also God► to be a Supreme Priest. Nowhis Son/the man who is also God► has forever become all that God intends him to be.