[This is part five of a deeper study of the article 6 Ways Christ was Better than the Law. To get better context and a link to the other parts, you can click there and read it first.]
The audience of the Hebrews letter was thinking about returning to Judaism. The writer confronts them in Hebrews 7 with a full discussion of Melchizedek. Any reader that wanted to be a true son of Abraham had to stop and give this a second look.
With just three verses in Genesis 14:18-20 and another sentence in Psalm 110:4, the Jews might not have given this a lot of attention. Once the writer reveals Melchizedek as the highest of priests, a priest that is also a king, the Jews could now accept Christ as a high priest. In fact his priesthood was even better than the Levitical priesthood.
For a little more development on Melchizedek, 8 Reasons Christ was like Melchizedek
takes a little closer look at the comparisons of him and Christ.