Tell me why the letter was written to the Hebrews.
To show the Jewish people the supremacy of the sacrifice of Jesus over the sacrifice of the Mosaic Law. Far more than that, but that is the main message of the book, that the blood of Jesus is far superior than the blood of bulls and goats.
Hebrews 9:12-14
King James Version
12 Neither by the blood of goats and calves, but by his own blood he entered in once into the holy place, having obtained eternal redemption for us.
13 For if the blood of bulls and of goats, and the ashes of an heifer sprinkling the unclean, sanctifieth to the purifying of the flesh:
14 How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God?
Hebrews 10
King James Version
10 For the law having a shadow of good things to come, and not the very image of the things, can never with those sacrifices which they offered year by year continually make the comers thereunto perfect.
2 For then would they not have ceased to be offered? because that the worshippers once purged should have had no more conscience of sins.
3 But in those sacrifices there is a remembrance again made of sins every year.
4 For it is not possible that the blood of bulls and of goats should take away sins.
5 Wherefore when he cometh into the world, he saith, Sacrifice and offering thou wouldest not, but a body hast thou prepared me:
6 In burnt offerings and sacrifices for sin thou hast had no pleasure.
7 Then said I, Lo, I come (in the volume of the book it is written of me,) to do thy will, O God.
8 Above when he said, Sacrifice and offering and burnt offerings and offering for sin thou wouldest not, neither hadst pleasure therein; which are offered by the law;
9 Then said he, Lo, I come to do thy will, O God. He taketh away the first, that he may establish the second.
10 By the which will we are sanctified through the offering of the body of Jesus Christ once for all.
11 And every priest standeth daily ministering and offering oftentimes the same sacrifices, which can never take away sins:
12 But this man, after he had offered one sacrifice for sins for ever, sat down on the right hand of God;
13 From henceforth expecting till his enemies be made his footstool.
14 For by one offering he hath perfected for ever them that are sanctified.