John Calvin Commentary Galatians 3:12

"and the law is not of faith; but, He that doeth them shall live in them." — Galatians 3:12 (ASV)

And the law is not of faith. The law evidently is not contrary to faith. Otherwise, God would be unlike Himself. But we must return to a principle already noticed: Paul’s language is modified by the present aspect of the case. The contradiction between the law and faith lies in the matter of justification. You will more easily unite fire and water than reconcile these two statements: that men are justified by faith, and that they are justified by the law. The law is not of faith; that is, it has a method of justifying a man which is wholly at variance with faith.

But the man who shall do these things. The difference lies in this: when a man fulfills the law, he is reckoned righteous by a legal righteousness, which Paul proves by a quotation from Moses (Leviticus 18:5). Now, what is the righteousness of faith? He defines it in the Epistle to the Romans:

If thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead,
thou shalt be saved (Romans 10:9).

And yet it does not follow from this that faith is inactive, or that it sets believers free from good works. For the present question is not whether believers ought to keep the law as far as they can (which is beyond all doubt), but whether they can obtain righteousness by works, which is impossible.

But since God promises life to the doers of the law, why does Paul affirm that they are not righteous? The reply to this objection is easy. There are none righteous by the works of the law, because there are none who do those works.

We admit that the doers of the law, if there were any such, would be righteous. However, since that is a conditional agreement, all are excluded from life, because no one performs the righteousness that he ought. We must remember what I have already stated: to do the law is not to obey it in part, but to fulfill everything that belongs to righteousness, and all are at the greatest distance from such perfection.