Why was there a need for a priest after the order of Melchizedek rather than after Aaron?
Because the Levitical priesthood could not bring perfection, and Gentiles could not approach God through a Jewish high priest. They needed a priest representing Gentiles, as Melchizedek did. Christ sprang from Judah, not Levi, so He was not eligible for the Aaronic order, but was made priest after Melchizedek by an endless life.
Les explains that if perfection came through the Levitical priesthood, under which Israel received the law, there would be no further need for another priest. But God promised a priest after the order of Melchizedek, not after Aaron, because Gentiles could not approach God through a Jewish high priest. They needed one who represents Gentiles, which is what Melchizedek pictured back in 2000 B.C. Also, the Lord Jesus sprang from the tribe of Judah, not Levi, so He was not eligible to be a priest after the order of Aaron. Instead, He was made priest after the similitude of Melchizedek, not by the law of a carnal commandment, but by the power of an endless life, a priest forever. This connects the high priest of the Gentile with the Most High God from start to finish.
If therefore perfection were by the Levitical priesthood, (for under it the people received the law,) what further need was there that another priest should rise after the order of Melchisedec, and not be called after the order of Aaron?