This is the section of Hebrews where the original audience is very clear. All the talk about a high priest is enough to make a Gentile, and most protestants more than a little creeped out. To really understand this section we must understand the role of the high priest in the Jewish tradition. The high priest is the one who would be the intermediary between God and the people. When there was sin to be atoned for, the high priest would offer sacrifice on behalf of the people. When there was prayer to be lifted, the high priest would burn incense and offer the prayers of the people. The Old Testament, more specific the Levitical, standard was to have only persons from the tribe of Levi to be the priests. The most glaring Old Testament exception is Melchizedek. He was a of God in the time of Abraham, before Aaron and the order of Levitical priests.
In the scriptures we meet Melchizedek before the giving of the law. Long before the captivity in Egypt, the exodus, and the giving of the law, God recognizes Melchizedek as a priest. Abraham also recognizes him and gives a tenth of the plunder from the recently won battle. This is a priest outside of the law. Jesus is a priest in this line, not the Levitical line. Outside of the giving of the law.
When the writer of Hebrews sets their sites on the law the Jewish audience would be outraged. The writer is saying that Jesus is bigger than the law, and the law has flaws in that it cannot make someone perfect. To say this would be controversial is among the top ten understatements of all time. It was through the law that righteousness was found, or so thought the Jews. The writer of Hebrews offers a different idea, Jesus.
It is through Jesus Christ that we are made right with God. Jesus as the High Priest. The one who offers sacrifice on our behalf, himself. The High Priest who goes to God on our behalf. Only through Jesus Christ can we be made perfect. The law failed in its attempt to present us to God without a blemish, Jesus Christ is the only way that can happen. Human priests are weak, and will let us down. Jesus, the ultimate priest will never let us down as he is perfect in every way and for all time.