When Paul said that the righteousness of the law is based on works,
he was quoting God and Moses from the Old Testament.

Romans 10:5 “Moses writes this about the righteousness that is by the law: “The person who does these things will live by them.”

Deuteronomy 6:25 “And if we are careful to obey ALL this law before the Lord our God, as he has commanded us, that will be ourrighteousness.””

Leviticus 18 “4 You must obey my laws and be careful to follow my decrees. I am the Lord your God. 5 Keep my decrees and laws, for the person who obeys them will live by them. I am the Lord.”

Deuteronomy 27:26 “Cursed is anyone who does not uphold the words of this law by carrying them out”

God told them to obey the Law to be the kingdom of priests.
Israel said that they would obey everything, before they even heard the 10 commandments. Some scholars say that this was self-righteousness on the part of Israel.

Exodus 19 “5 Now if you obey me fully and keep my covenant, then out of all nations you will be my treasured possession. Although the whole earth is mine, 6 you will be for me a kingdom of priests and a holy nation.’ These are the words you are to speak to the Israelites.” 7 So Moses went back and summoned the elders of the people and set before them all the words the Lord had commanded him to speak. 8 The people all responded together, “We will do everything the Lord has said.” So Moses brought their answer back to the Lord.”

On the day that they received the law, 3000 died due to idol-worship – something that they had not even done before the day the law came.We never saw Abraham’s children worshipping idols, until the law came!
The law increases sin and it brings death and condemnation.
Their self-righteousness backfired in just one day.
Paul calls the ten commandment (law written on stone) as the ministry of death and condemnation. It was the Letter that kills. But Jesus brings Eternal life and Righteousness in the New Covenant (the Spirit of LIFE)

If we relate to God by our works then we will be afraid of Him but when we relate to God based on what Jesus did, then there will be JOY and PEACE:

Hebrews 12:18-24 “You have not come to a mountain (Sinai) that can be touched and that is burning with fire; to darkness, gloom and storm; to a trumpet blast or to such a voice speaking words that those who heard it begged that no further word be spoken to them, because they could not bear what was commanded: “If even an animal touches the mountain, it must be stoned to death.” The sight was so terrifying that Moses said, “I am trembling with fear. But you have come to Mount Zion, to the city of the living God, the heavenly Jerusalem. You have come to thousands upon thousands of angels in joyful assembly, to the church of the firstborn, whose names are written in heaven. You have come to God, the Judge of all, to the spirits of the righteous made perfect, to Jesus the mediator of a new covenant, and to the sprinkled blood that speaks a better word than the blood of Abel.“

• When the 10 commandments were given on Mt Sinai, the people were terrified with FEAR because the Law demanded perfection & exposed their sins, condemning them. (Mt.Sinai=Old-Covenant. Galatians 4:25-26).
• But when Jesus died on the Cross, the New Covenant came with JOY in heaven because the blood of Christ says that we are FORGIVEN ALL sin and RIGHTEOUS by His death/resurrection, not our works! 
• When the Ten commandments were given, the people could not dare go up to the Mountain to see God. If they touched the mountain they would die because their sins were exposed. But when Jesus came, He came down the mountain, He touched/healed the leper. The Holy Spirit came down from heaven and lives inside us who believed in Jesus because our sins are forgiven! God touched us to save us in the New Covenant.

2 Corinthians 3:3-18 “You show that you are a letter from Christ, the result of our ministry, written not with ink but with the Spirit of the living God, not on tablets of stone but on tablets of human hearts. Such confidence we have through Christ before God. Not that we are competent in ourselves to claim anything for ourselves, but our competence comes from God. He has made us competent as ministers of a new covenant—not of the letter but of the Spirit; for the letter kills, but the Spirit gives life. Now if the ministry that brought death, which was engraved in letters on stone, came with glory, so that the Israelites could not look steadily at the face of Moses because of its glory, transitory though it was, will not the ministry of the Spirit be even more glorious? If the ministry that brought condemnation was glorious, how much more glorious is the ministry that brings righteousness! For what was glorious has no glory now in comparison with the surpassing glory. And if what was transitory came with glory, how much greater is the glory of that which lasts! Therefore, since we have such a hope, we are very bold. We are not like Moses, who would put a veil over his face to prevent the Israelites from seeing the end of what was passing away. But their minds were made dull, for to this day the same veil remains when the old covenant is read. It has not been removed, because only in Christ is it taken away. Even to this day when Moses is read, a veil covers their hearts. But whenever anyone TURNS to the LORD, the veil is taken away. Now the Lord is the Spirit, and where the Spirit of the Lord is, there is freedom. And we all, who with unveiled faces CONTEMPLATE the Lord’s GLORY, are being transformed into his image with ever-increasing glory, which comes from the Lord, who is the Spirit.”

• The Ten Commandments had glory but brought death and condemnation. 3000 DIED on the day Israel received the 10 commandments just because they broke one commandment (worshipping idols).
• But the New Covenant has GREATER glory because Jesus gives us Righteousness as a gift! 3000 Jews who committed the greater sin of crucifying Jesus, were SAVED when the Holy Spirit came (Acts 2:36-41).
• The Christian is not guided by the Ten Commandments but by the GRACE of JESUS (Galatians 5:18).
  • We keep LOOKING to JESUS who made us Righteous and Holy.
• Christianity is not Laws written on stone but knowing Jesus and His LOVE written in our hearts.
• John 1:16-18 “Out of his fullness we have all received grace in place of grace already given. For the law was given through Moses; grace and truth came through Jesus Christ. No one has ever seen God, but the one and only Son, who is himself God and is in closest relationship with the Father, has made him known.”
  • Jesus came to reveal the Father’s Grace upon Grace.
• The law brings condemnation because it demands perfection (Romans 10:5, Galatians 3:10-12)
• But Jesus gives GRACE because He forgave us ALL sin and made us perfect by FAITH.

Why did God give the law?

Paul explains that it was done to silence the self-righteousness of men and to show them that they are sinners who need salvation.

Romans 3 “19 Now we know that whatever the law says, it says to those who are under the law, so that every mouth may be silenced and the whole world held accountable to God. 20 Therefore no one will be declared righteous in God’s sight by the works of the law; rather, through the law we become conscious of our sin.

Israel was trapped under the custody of the law for 1500 years until Jesus would come to set them free.

Galatians 3 19 Why, then, was the law given at all? It was added because of transgressions until the Seed to whom the promise referred had come. The law was given through angels and entrusted to a mediator. 20 A mediator, however, implies more than one party; but God is one. 21 Is the law, therefore, opposed to the promises of God? Absolutely not! For if a law had been given that could impart life, then righteousness would certainly have come by the law. 22 But Scripture has locked up everything under the control of sin, so that what was promised, being given through faith in Jesus Christ, might be given to those who believe. 23 Before the coming of this faith, we were held in custody under the law, locked up until the faith that was to come would be revealed. 24 So the law was our guardian until Christ came that we might be justified by faith. 25 Now that this faith has come, we are no longer under a guardian. 26 So in Christ Jesus you are all children of God through faith

Paul said that the law was the POWER of sin. The law increased sin so that the Jews would despair and call upon Jesus for salvation:

1 Corinthians 15 “56 The sting of death is sin, and the power of sin is the law. 57 But thanks be to God! He gives us the victory through our Lord Jesus Christ.”

Paul himself experienced the increase of sin when he tried to keep the 10 commandments. As a result, he says that Jesus is the one who saves from that state of despair under the law.

Romans 7 “7 What shall we say, then? Is the law sinful? Certainly not! Nevertheless, I would not have known what sin was had it not been for the law. For I would not have known what coveting really was if the law had not said, “You shall not covet.” 8 But sin, seizing the opportunity afforded by the commandment, produced in me every kind of coveting. For apart from the law, sin was dead. 9 Once I was alive apart from the law; but when the commandment came, sin sprang to life and I died. 10 I found that the very commandment that was intended to bring life actually brought death. 11 For sin, seizing the opportunity afforded by the commandment, deceived me, and through the commandment put me to death. 12 So then, the law is holy, and the commandment is holy, righteous and good.13 Did that which is good, then, become death to me? By no means! Nevertheless, in order that sin might be recognized as sin, it used what is good to bring about my death, so that through the commandment sin might become utterly sinful. 14 We know that the law is spiritual; but I am unspiritual, sold as a slave to sin. 15 I do not understand what I do. For what I want to do I do not do, but what I hate I do. 16 And if I do what I do not want to do, I agree that the law is good. 17 As it is, it is no longer I myself who do it, but it is sin living in me. 18 For I know that good itself does not dwell in me, that is, in my sinful nature. For I have the desire to do what is good, but I cannot carry it out. 19 For I do not do the good I want to do, but the evil I do not want to do—this I keep on doing. 20 Now if I do what I do not want to do, it is no longer I who do it, but it is sin living in me that does it.21 So I find this law at work: Although I want to do good, evil is right there with me. 22 For in my inner being I delight in God’s law; 23 but I see another law at work in me, waging war against the law of my mind and making me a prisoner of the law of sin at work within me. 24 What a wretched man I am! Who will rescue me from this body that is subject to death? 25 Thanks be to God, who delivers me through Jesus Christ our Lord!”

The entire purpose of the law was this:- to shut the mouth of self-righteous people showing that nobody is righteous by the law (because the law demands perfection).- to make sin increase so that they would be conscious of sin- as a result they would come to Jesus to be saved by faithWhen law increased the sins, the Grace of God came on the cross even more!

Romans 5:20 “The law was brought in so that the trespass might increase. But where sin increased, grace increased all the more,“

 Once we come to Christ, we are no longer under the law.- we are then under grace, and sin will not rule over us.- we have been set free by Jesus.

Romans 6:14 “For sin shall no longer be your master, because you are not under the law, but under grace.”

So then what does Paul mean by “the license to sin” ?It’s not about grace. It’s actually about going back to law and/or unbelief.

Romans 6 “What shall we say, then? Shall we go on sinning so that grace may increase? 2 By no means! We are those who have died to sin; how can we live in it any longer? “

Because it is the law that increases sin for Jews as he mentioned just few verses before.

The unbelief in Jesus/God increases sin for Gentiles not under law.

Romans 1:21-24″ For although they (Gentiles) knew God, they neither glorified him as God nor gave thanks to him, but their thinking became futile and their foolish hearts were darkened. ²² Although they claimed to be wise, they became fools ²³ and exchanged the glory of the immortal God for images made to look like a mortal human being and birds and animals and reptiles²⁴ Therefore God gave them over in the sinful desires of their hearts to sexual impurity for the degrading of their bodies with one another. “

The Grace of God cannot increase sin as Paul clearly testified in Romans 6:14.
Being dead to sin means being dead to the law.
But if a person goes back to the law/unbelief, sin will increase in their lives!
That is the meaning of “go on sinning”…the license to sin was to trust in the works of the law/trust in something other Jesus. It was to rebuild what was once destroyed as Paul says here:

Galatians 2 “15 “We who are Jews by birth and not sinful Gentiles 16 know that a person is not justified by the works of the law, but by faith in Jesus Christ. So we, too, have put our faith in Christ Jesus that we may be justified by faith in Christ and not by the works of the law, because by the works of the law no one will be justified. 17 “But if, in seeking to be justified in Christ, we Jews find ourselves also among the sinners, doesn’t that mean that Christ promotes sin? Absolutely not! 18 If I rebuild what I destroyed, then I really would be a lawbreaker. 19 “For through the law I died to the law so that I might live for God. 20 I have been crucified with Christ and I no longer live, but Christ lives in me. The life I now live in the body, I live by faith in the Son of God, who loved me and gave himself for me. 21 I do not set aside the grace of God, for if righteousness could be gained through the law, Christ died for nothing!”

Who were the ones who sinned the most, killing Jesus and the Apostles? It was those who trusted in the law instead of Jesus.
On the day the Law was given, 3000 died because of one sin (worshipping idols). But when Jesus (Grace came), 3000 were saved on the Day of Pentecost when the Holy Spirit was given, even after committing the worst sin of crucifying Jesus. The law increased sin but Grace increased even more!

John 1:17 “For the law was given through Moses; grace and truth came through Jesus Christ.”

Paul says that those who trust in Jesus have died to the law and have been set free from sin. 

Romans 7 “4 So, my brothers and sisters, you also died to the law through the body of Christ, that you might belong to another, to him who was raised from the dead, in order that we might bear fruit for God. 5 For when we were in the realm of the flesh, the sinful passions aroused by the law were at work in us, so that we bore fruit for death. 6 But now, by dying to what once bound us, we have been released from the law so that we serve in the new way of the Spirit, and not in the old way of the written code.”

Jesus came to release people from the law so that they would bear the fruit of the Spirit by the Grace of God through faith apart from works.
Paul called himself the chief of sinners. When was he the chief of sinners? This was when he was trusting in the law and became the chief persecutor of Christians.

1 Timothy 1 “12 I thank Christ Jesus our Lord, who has given me strength, that he considered me trustworthy, appointing me to his service. 13 Even though I was once a blasphemer and a persecutor and a violent man, I was shown mercy because I acted in ignorance and unbelief. 14 The grace of our Lord was poured out on me abundantly, along with the faith and love that are in Christ Jesus. 15 Here is a trustworthy saying that deserves full acceptance: Christ Jesus came into the world to save sinners—of whom I am the worst. 16 But for that very reason I was shown mercy so that in me, the worst of sinners, Christ Jesus might display his immense patience as an example for those who would believe in him and receive eternal life.”

Philippians 3 “If someone else thinks they have reasons to put confidence in the flesh, I have more: 5 circumcised on the eighth day, of the people of Israel, of the tribe of Benjamin, a Hebrew of Hebrews; in regard to the law, a Pharisee; 6 as for zeal, persecuting the church; as for righteousness based on the law, faultless. 7 But whatever were gains to me I now consider loss for the sake of Christ. 8 What is more, I consider everything a loss because of the surpassing worth of knowing Christ Jesus my Lord, for whose sake I have lost all things. I consider them garbage, that I may gain Christ 9 and be found in him, not having a righteousness of my own that comes from the law, but that which is through faith in Christ—the righteousness that comes from God on the basis of faith.”

If we look at the root of sin, it was Adam’s self-righteousness, trying to be like God by knowing right and wrong.

It was unbelief in God’s goodness.

The first sin was self-righteousness. The sin of Israel was self-righteousness. The sin of Gentiles was unbelief.

Trusting in the works of the law or unbelief in Jesus, results in the works of the flesh, all kinds of sin.

But trusting in Jesus Christ, makes us righteous by faith, and this produces the fruit of the Spirit