Galatians 3:10 For as many as are of the works of the law are under the curse: for it is written, Cursed is every one that continueth not in all things which are written in the book of the law to do them.I think I agree with HP that the Law can indeed be kept - Paul kept it, or so he claims in Phillipians.
Remember - the Law of Moses is only for the Jews. So for Paul to say what he says in the text you give, he must have a concept of sin that extends beyond breaking the Law of Moses. In short, even if you keep the Law of Moses, you could still sin.
Paul says that it is impossible to keep the law. In order to keep the law one would have to continue from birth to death in keeping all the Jewish laws, without breaking one during the entirety of his life. There are hundreds of Levitical laws, ceremonnial laws, civil laws, etc. Just one law broken, one time in one's life would curse a person--condemn him to hell for all eternity.
"Cursed is every one that continues not in ALL things that are written in the BOOK of the law to do them." That is a lot of law.
The only answer:
Galatians 3:11 But that no man is justified by the law in the sight of God, it is evident: for, The just shall live by faith.
--This is part of the answer. The law shows that we are sinners. It can't save. It can't justify. We can't keep it. Because we can't keep it, it can't save us, and therefore we need a Savior. That is precisely why Christ came. No man can keep the law.
Galatians 3:13 Christ hath redeemed us from the curse of the law, being made a curse for us: for it is written, Cursed is every one that hangeth on a tree:
--Christ has redeemed us from the curse of the law. He took our place on the cross, and paid a penalty that we could never pay. He was made a curse for us. It was the only way that that penalty for sin could be paid; that the demands of the law could be fulfilled.
And thus the sacrifice of Christ must be accepted by faith, and not of works.
Galatians 3:12 And the law is not of faith: but, The man that doeth them shall live in them.
--What a terrible way to live: under the law--by works, and not of grace--the grace that Christ alone offers which must be accepted by faith alone.
Galatians 3:14 That the blessing of Abraham might come on the Gentiles through Jesus Christ; that we might receive the promise of the Spirit through faith.