Who is better, the Jews or the Gentiles? Answer: We are all under sin and fall short of the glory of God. Whether we are under the law or not, we will all be held accountable to Him. No Jew or Gentile can become righteous from obeying the law. Rather, through the law we become conscious of sin.
What does that mean? I'll put it in 3rd grade terms. When students come at the beginning of the year, many are still nose-pickers. They don't know that they shouldn't do it until someone tells them (either me or a rude peer). When they are aware that it's wrong, they will begin to hide it better. Some pickers cover their noses with their other hand, or the smarter ones will even put a book in front of their faces.
Because we were all nose-pickers (or sinners), we had to be made right somehow. This righteous from God (that is, Jesus) was sent as the ultimate sacrifice for our wrongs. There is no boasting. Some might say, "Well, I don't pick my nose anymore." But your nosepicking in the past has to be made right. Still others use the argument, "Well, I'm forgiven so I can continue picking my nose because my wrongs enhance God's righteousness." To which I would say, Stop picking your nose!
In Chapter 4 Paul spends the whole chapter describing Abraham. Abe wasn't considered righteous based on his actions, but only because of his strong faith.
For if those who live by law are heirs, faith has no value and the promise is worthless, because law brings wrath. But where there is no law there is no transgression. ~Romans 4:14-15Because Jesus died for our sins, we're are no longer bound under the law. Our sins are wiped clean and there is no wrath. We are now called to live by faith in a God who loved us so much that He sent His Son to die for us. And if we are truly living by faith, why would we ever want to continue messing around with our former sins?