Purpose of the Law - To Humble Us & Point Us to the Gospel

Now it is evident that no one is justified before God by the law, for "The righteous shall live by faith."
But the law is not of faith, rather "The one who does them shall live by them." 
- Galatians 3:11-12

“Notice that Paul explains his meaning at some length here for us to comprehend why he separates the righteousness of the law and the righteousness of faith, showing us that they are incompatible and can no more be mixed together than fire and water. Not that there is any contradiction between the law and the gospel (as I have already made clear), for we know that they both proceed from the same God. But we must remember God’s purposes, as we have said all along. By giving us the righteousness of the law, he intended to humble us. Next, we will come before him realising we are condemned; this we would never have done if he had not revealed to us our own poverty. When we read that God promises justification if we serve him aright, he is saying in effect, ‘Poor creatures, what worth or value do you have in and of yourselves? Weigh up my commandments and consider what they involve, and then reflect upon how each of you have lived. This will make you feel as if you could drown in self-despair.’ Yet, though God speaks in this vein, he also grants a remedy —‘Come’, he says, ‘to the teachings of the gospel’. And what are they? Paul quotes the expression of Habakkuk, from chapter two and the fourth verse: ‘The just shall live by his faith’...

“[Paul] always taught that faith leads us to find salvation in God alone. The law, though it may appear to be teaching something very different, actually shows us that there is no life in us at all, if we understand it aright. The law says, ‘Work hard and do what you can to obtain paradise.’ Why does it say this? Not to feed man’s vain confidence in his own merits —certainly not! Rather, to prepare us to receive the grace of the Lord Jesus Christ in humility.”

John Calvin. Sermon on Galatians 3:11-12