Melchizedek towers out of the past--without record of family ties, no account of beginning or end. In this way he is like the Son of God, one huge priestly presence dominating the landscape always.
Priests descended from Levi are commanded by law to collect tithes from the people, even though they are all more or less equals, priests and people, having a common father in Abraham.
If the priesthood of Levi and Aaron, which provided the framework for the giving of the law, could really make people perfect, there wouldn't have been need for a new priesthood like that of Melchizedek.
But then God intervened and called this new, permanent priesthood into being with an added promise: God gave his word; he won't take it back: "You're the permanent priest."
So now we have a high priest who perfectly fits our needs: completely holy, uncompromised by sin, with authority extending as high as God's presence in heaven itself.
Unlike the other high priests, he doesn't have to offer sacrifices for his own sins every day before he can get around to us and our sins. He's done it, once and for all: offered up himself as the sacrifice.
The law appoints as high priests men who are never able to get the job done right. But this intervening command of God, which came later, appoints the Son, who is absolutely, eternally perfect.