Paul is explaining to the Jews present that they were never justified by the works they did under the law. They had spent their lives seeking to be justified but had come up short because the law cannot justify anyone. So, if the law was unable to justify anyone, was God actually causing everyone to sin when they were under the law? Paul says that would never happen. The law was not given to make men fail, but to teach them that they could not justify themselves by works.
19 Now we know that whatever the Law says, it speaks to those who are under the Law, so that every mouth may be closed and all the world may become accountable to God; 20 because by the works of the Law no flesh will be justified in His sight; for through the Law comes the knowledge of sin.—Romans 3:19, 20 (NASB)
So, the law was given that all men might know that they needed a redeemer. That is why Jesus Christ died on the cross and was resurrected. Because of that act of love by God the Father and Jesus the Son, we are all now under grace, not the law. Now, we are all saved by grace through faith. There is a time, place and need for works, but they are not a part of salvation. We are justified by the blood of Jesus, we are in the process of being sanctified, and one day, we will be glorified. Not because we earned it, but, because Jesus, with His blood, has paid the full price for all of us!