3. Sacrifice of Christ
One aspect of note in Leviticus 9 is that the high priest had to not only make offerings for the people, but had to do so for himself first,
Lev 9:7: Moses said to Aaron, "Draw near to the altar, and offer your sin offering, and your burnt offering, and make atonement for yourself, and for the people; and offer the offering of the people, and make atonement for them; as Yahweh commanded." WEB
This is different to what happened in the surrounding nations, with the worship to their gods. In those cases, the priests were made to be above the people and somehow closer to the gods that they didn't need the humility of sacrificing for their own sins.
However, here we see the different role of the priests to the God of Israel.
In the book of Hebrews, we see a contrast between the sacrifice made by Jesus, and that offered up by the priests. Speaking of Jesus,
Heb 7:26: For such a high priest was fitting for us: holy, guiltless, undefiled, separated from sinners, and made higher than the heavens; 27. who doesn't need, like those high priests, to daily offer up sacrifices, first for his own sins, and then for the sins of the people. For this he did once for all, when he offered up himself. 28. For the law appoints men as high priests who have weakness, but the word of the oath which came after the law appoints a Son forever who has been perfected. WEB
Dying with Christ
It is of course through Jesus that we have a great gift. We get to participate in a sacrifice that is lasting. But to do that, we really need to be a part of it. In Galatians, we read of how this involves taking on the life of Jesus,
Gal 2:19: For I, through the law, died to the law, that I might live to God. 20. I have been crucified with Christ, and it is no longer I that live, but Christ living in me. That life which I now live in the flesh, I live by faith in the Son of God, who loved me, and gave himself up for me. 21. I don't make void the grace of God. For if righteousness is through the law, then Christ died for nothing!" WEB
So just like the Israelites and their offerings, there is a removal of individuality and choice. It is no longer ourselves that is living, and instead we need to be new people with our individuality being part of Christ.