The offense of the cross was that it turned on its head every attempt to be righteous through self-effort and keeping of the law. Paul, in Romans, makes it very clear that those who sought righteousness by law did not attain it, but those who sought it by faith attained it. In Romans, Corinthians, and Galatians stronger than in his other letters, Paul says that the law was a ministration of death and was intended to make sin come alive, to show man just how sinful he was. Trying to keep the law never produced righteousness, nor could it ever. It is had, according to Hebrews, then Christ died for nothing.
That being said, it has been put forward in this thread that sin is the breaking of the law, the commandment. I agree with that. It is Biblical. But it is important that we make a distinction that Paul made in Romans 6. There are two words for sin that he uses. One is a noun, the other a verb. The noun is the body of sin that dwelled in man. The verb is the action of breaking the law. Paul says that we, through dying with Christ and being resurrected with Him, have been set free from the body of sin. We are dead to sin. This means totally dead to sin; dead to its stain, its condemnation, its shame, and its power over us. Since I am born again, I am freed from sin just like a man whose wife has died is freed from his marriage (see Rom. 7). I have been declared righteous through the blood of Jesus. His righteousness has been imputed unto me and I am now just as righteous as Jesus. See 1 Cor. 1:30 and 2 Cor. 5:21.
So if I commit an act of sin, it does not reintroduce to me the body of sin. I am dead to that and have been freed from it. Jesus is my propitiation, not myself. So Paul in Rom. 6 says, since you have been set free from sin (noun), don't yield your members to sin (verb or acts of sin). Don't you know that when you do that, you willingly submit yourself as a servant to that sin.
A couple verses that were alluded to that I think are worth noting. Hebrews does not say that willingly committing a sin causes you to become reprobate, or unable to be resaved. The falling away that is referred to here has to be interpreted in the context of the rest of the letter. Jews who converted to Christianity were under IMMENSE pressure to return to the law and give up Jesus as Messiah and savior. They were castigated by their families, friends, communities, and all of Jewish society. Paul tells them that if they would decide to reject Christ and go back to trying to be righteous by dead works, there was no more sacrifice but a looking forward to the judgment of God. Why? Because they rejected righteousness and relationship by faith and returned to the enmity of the law.
Tne other is "by ye perfect even as your Father in heaven is perfect." If you read the context of this verse, it goes like this. You have heard the Pharisees say that if you want to be righteous then you need to do this or that. But I say that this picture of righteousness is only a shadow of what God's righteousness is like. Keeping the law does not make you righteous in yourself. If you want to be righteous by keeping laws, then you have to be righteous like God. In other words, you have to be perfect like He is perfect, not like the law, only a shadow of Him.
So can we commit an act of sin? Absolutely. We can miss the mark. Does this sully our spirit or cause us to be a sinner? Absolutely not. So whosoever is born of God does not sin(the noun), because he is born again (has God's seed in him). So he cannot commit acts of sin (verb) because he is born of God.
We have been so sensitized to sin and so desensitized to the power of God in the rebirth and the work of the Holy Spirit in our lives. We have preached the gospel as if it is all about going to heaven and hell, which has done much to destroy the work of God in men. We have become, as a result, so focused on whether an action is sin or not. But if the power of God is in us and we realize what sonship, intimacy, the power of the Holy Spirit, and walking in the Spirit and not the flesh is all about, we will begin to walk in levels of holiness and purity that we could only dream of when we were focused on sin and our own actions.
Self-effort can only produce death since it is enmity against God and one of the things God called us to repent of. When we focus on sin and trying to overcome it we only strengthen it in our lives. But when we focus on what God has done for us in Christ, we begin to walk as Jeremiah prophesied, with the law (the true righteous nature of God) written on our hearts. Our actions will follow this law of the Spirit of life in Christ Jesus.
Do I miss the mark at times? Absolutely. But I never dwell on it. I have learned to bring that to the Lord and ask Him to show me what is wrong and how to bring myself back into His ability and not my own in that area. Perhaps there are things that I have to do (acts of obedience) to distance myself from influences that led to me missing the mark. This is what a person who is born again will naturally do. Sin is not inevitable. I am reaching the point where I no longer give sin a second thought in my daily life. I go through each day seeking Him, walking with Him, communing with Him, and learning what His righteousness lived out through my life looks like.
Just my take on the topic.