The writer of Hebrews begins his argument concerning the superiority of Christ to everything by discussing his superiority angels. Why start with the angels?
Angels were very popular in Jewish mythology from the second century B.C. through the first century A.D. A whole hierarchy of angels was developed along with some theological teachings that were not present in the Old Testament. In the re-telling of Biblical stories writers often had angels performing acts that were acts of God in the Hebrew Bible. Although the imagery is found in Daniel 10, the appearance of angels as glowing white, fiery, glowing, etc. was developed during this time as well.
What is more, the angels are associated with the giving of the Law in early Judaism. This tradition appears in the Hebrew Bible as early as Deut 33:2, although the “holy ones” merely accompany the Lord as he arrives at Sinai. Stephen refers to the Law as “delivered by angels” in Acts 7:53. The book of Jubilees predates Hebrews clearly has the belief that an angel wrote a text for Moses:
Jubilees 1.27-28 And He said to the angel of the presence: ‘Write for Moses from the beginning of creation till My sanctuary has been built among them for all eternity.’ (Charles)
This tradition is found in later Judaism as well: “The presence of angels at the event of the giving of the law was a favourite bit of embroidery in rabbinic tradition, and was meant to enhance the glory of Sinai” (H. Schoeps, Paul, 182). The emphasis in this literature is on the angels as intermediaries, delivering the Law to Moses. When God revealed himself to Moses, he used angels.
Since the writer of Hebrews began his book by saying that God is new revealing himself through his Jesus, it is possible a Jewish reader might think of Jesus as an angel, like a Michael or Gabriel. He must therefore begin by showing that Jesus is something other than an angel, he is “Song of God.”
One last observation: Is this a “difference” between Jewish Christian literature and the Pauline Letters? Perhaps not. While Paul cannot be accused of emphasizing angels, he does use the same sort of language as Stephen in Gal 3:19: The law was “put in place through angels” (ESV).