It was the Judaizing teachers making the false claim that the Gentiles had to be circumcised to be saved. Therefore Paul's point to those Galatians was that the OT law of Moses cannot completely justify one before God. Complete justification can be found in the NT gospel not the OT law of Moses therefore those Galatians had fallen from grace for leaving the NT gospel.
There is an important theme that we must obey God rather than man, so we must be careful not to take something that was only against obey man's laws and being against obeying God's Law. As such, if what the Judaizers were wanting to require Gentiles to do isn't required by the God's Law, then it would be a mistake to take an argument that was against a man-made requirement as being an argument against obeying God's Law. Paul made the point that we aren't justified by the Mosaic Law, but the Law was never given for that purpose in the first place, and trying to become justified by obeying the Law has always been a fundamental misunderstanding and a perversion of it. It does not follow that because we don't need to obey God's commands in order to become justified that therefore don't need to obey them.
Under the NT gospel we have the blood of Christ to remit all sins whereby God remembers sins no more.
Yet for those that lived under the OT law of Moses did not have the blood of Christ, but the blood of bulls and goats that could not remit all sins and there was a remembrance of sins (Hebrews 10:1-4). So in what way could one under the OT law ever be completely justified before God? Therefore the only way a Jew could be completely justified before God was by flawless law keeping. Since sin is transgression of the law, therefore if the Jew could keep all OT law perfectly then he would have no sin and not having any sin he could then stand before God totally justified. This is the ONLY means one could ever by totally justified before God under the OT law. Yet the Jew would always eventually sin making complete justification under the OT law impossible.
Again, the one and only way that there has ever been to become justified is by faith and justification through perfect obedience to God's Law was never a means that was offered. If it were possible for someone to live in perfect obedience to the Law yet without having faith, then they still would not be justified because justification comes only through faith. Abraham was justified by faith and he looked forward in faith to Messiah's day and was glad (John 8:56), so people of the OT were justified by faith in the same way we are, which means that they lived in obedience to God's Law by the same faith, as we should.
This is why Paul would say in Gal 3:11 "But that no man is justified by the law in the sight of God,..." for no man could keep that OT law perfectly.
Other points Paul made to those Galatains that the OT law cannot justify the before God:
Gal 5:3 "For I testify again to every man that is circumcised, that he is a debtor to do the whole law."
Justification required on to keep the WHOLE law perfectly. Those Galatians could not just be circumcised and keep a few of the OT laws to be jsutified before God but must keep all of it....perfectly...flawlessly.
Gal 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."
Not keeping the whole OT law perfectly brought a curse upon the Jew. The impossibility of not being able to do "all things" made total justification before God impossible.
Gal 3:12 "And the law is not of faith: but, The man that doeth them shall live in them."
Paul plainly says the law is NOT OF FAITH. Again, total, complete justification under the OT law required flawless keeping of all the law. The reason no man under the law is not justified before God (verse 11) and the reason the law is not of faith is found in verse 10> "Cursed is every one that CONTINUETH NOT IN ALL THINGS..of the law"
Paul quotes Leviticus 18:5 here in verse 12 showing, to be totally justified under the OT law, faith did not matter.... just do the law and live. As Paul puts it "the man that doeth them (all OT laws) shall live in them".
I made the point in the post that you responded to that the phrase "works of law" does not refer to a definitive set of laws, such as
the Law of Moses and
the Book of the Law, which you seem to have ignored. In Galatians 3:10-12, Paul was speak about works of law, which are not of faith, and contrasting it with the Book of the Law, which is of faith in God (Matthew 23:23). Those who relied on man-made works of the law were not living by faith in God and thus were failing to do everything in the Book of the Law. I made that point that Hebrews 11 is full of examples of people who lived by faith by living in obedience to God's commands, so obedience to the Book of the Law is how the righteous live by faith. The works of the law are not of faith, but rather and the one who obeys the Law shall live by it by faith.
I also showed in the post that you responded to how the Mosaic Law was straightforwardly of faith in God to lead us in how we should live. However. if you nevertheless insist on continuing to Paul as speaking about the Mosaic Law not being of faith, then you would be interpreting him as directly contradicting Jesus, so you would need to make a decision about who has the greater authority and who to follow. I again made the point in my previous post that those Gentiles who were agreeing to become circumcised were becoming Jewish proselytes and were agree to live as Jews according to all of their man-made oral laws, traditions, rulings, and fences, and this is the same point Paul was making in Galatians 5:3.
But God was never looking for those OT characters to be justified by perfect adherence to the law but be justified by an obedient faith as Abraham had. Paul told those Galatians "Christ hath redeemed us from the curse of the law, being made a curse for us..." Christ took the OT law out of the way on His cross replacing it with His NT law that does not required flawless law keeping to be totally, completely justified but a simple obedient faith. Paul's point to those Galatians is why do you want to go to the OT law to find justification when you cannot be justified before God by that law that requires sinless perfection but can be justified by the NT gospel by an simple obedient faith
I completely agree that God was never looking for anyone in the OT to become justified by perfect adherence to the Law, but to become justified by the same faith Abraham had, and by the same faith Abraham lived in obedience to God's commands. According to Deuteronomy 30:15-30, the Law brings life and a blessing for obedience and death and a curse for disobedience, so being set free from the curse of the Law is being set free from living in disobedience to it so that we can be free to live a life of blessing in obedience to it.
Jesus was born under the Law and according to Deuteronomy 4:2, it is a sin to add or subtract to it, so if you think that Jesus disagreed with what the Father commanded and replaced the OT Law with his own, then you should consider him to have sinned and you should therefore not consider him to be your Savior. On the contrary, Jesus said that not the least part would disappear from the Law until heaven and earth passed away and all is accomplished, and he gave a warning to those who would relax the leasts part of the law or teach other to do so (Matthew 5:17-19). Jesus said that his teachings was not his own, but that of the Father (John 7:16), so he did not add his own commands, but rather he fully taught obedience to the Mosaic Law, and even if he had said nothing, he would have taught full obedience to it by example, and we are told to follow his example. Again, the OT Law never requires flawless keeping in order to become justified, but rather they were justified by faith and by the same faith they lived in obedience to the Law.
A mistake many make is they claim NO WORKS of any kind justifies one bofore God when Paul is limiting "works" here to works of the OT law and NOT eliminating a faithful obedience
It appears that you have a grasp on the concept of faithful obedience or the obedience that faith requires, but it seems odd to me that you contrasted that with the OT Law instead of also apply that concept to OT Law. We have not been justified by doing good works, but for the purpose of doing them (Ephesians 2:8-10) and it is OT Scripture that equips us to do every good work (2 Timothy 3:16-17). The Mosaic Law was given as instructions for how to do what is holy, righteous, and good and how to avoid sin (Romans 7:12, Romans 7:7) and our salvation involves being trained by grace to do what is godly, righteous, and good and trained to renounce doing what is ungodly and sinful. (Titus 2:11-13). Furthermore Titus 2:14 does not say that Christ gave himself to redeem us from the Law, but to redeem us from Lawlessness and to purify for himself a people who are zealous for doing good works, which is why the Jews in Acts 21:20 became zealous for the Law.