Romans 7:1 — Know ye not, brethren, (for I speak to them that know the law,) how that the law hath dominion over a man as long as he liveth?
In Romans 6:15, Paul asks if we should sin because we're not under the law but under grace. In the rest of chapter 6, he answered the second part of the question (under grace). Now he goes back to the first part (not under the law).
The point of chapter seven is that sanctification doesn't come by law any more than salvation does.
Chapter six showed that we were dead to sin. Now chapter seven shows that we are dead to the law. Chapter six shows how we are delivered from sin as our master. Chapter seven shows how we are delivered from the law as our husband.
Paul shows the defeat of trying to keep the law by his use of personal pronouns.
I — 30 times
Me — 12 times
My — 4 times
Myself — 1 time
Law — 23 times
This demonstrates failure to live out Galatians 2:20 — I am crucified with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith of the Son of God, who loved me, and gave Himself for me.
law (in this verse) — law as such in the abstract
Out of the fifth verse a question arises. "The sinful passions which were through the law", Paul says. If the inclination to sin comes from the law, then isn't the law something sinful? Paul answers that question in the second division by affirming that the law is holy. Look at the twelfth verse for a clear statement of this fact.
But another question will emerge right here. If the law is holy, then why cannot the law make the Christian holy? The answer follows logically. "We know that the law is spiritual; but I am carnal" (7:14), and that is why a good and holy law cannot make a person holy. Not because there is anything the matter with the law, but because the person is "carnal." — Alva J. McClain, Romans: The Gospel of God's Grace, pg. 152.