Paul spoke about multiple different categories of law other than the Law of God, such as the law of sin and works of the law, so it should at least be worth investigating the issue of which law he was referring to us as not being under out of all of the categories of law that he spoke about. For example, in Romans 7:25-8:2, he contrasted the Law of God with the law of sin and contrasted the Law of the Spirit with the law of sin and death. In Romans 3:27, Paul contrasted a law of works with a law of faith, and in Romans 3:31 and Galatians 3:10-12, he contrasted a law that our faith upholds with works of the law that are not of faith.
In Romans 7:7, Paul said that the Law of God is not sinful, but is how we know what sin is, and when our sin is revealed, then that leads us to repent and causes sin to decrease. Furthermore, in Romans 7:12, he said the it is holy, righteous, and good, so it is a law where holiness, righteousness, and goodness have dominion over us. In contrast, the law of sin stirs up sinful passions in order to bear fruit unto death, so it is sinful, it causes sin to increase, and it is a law where sin has dominion over us. In Romans 6:14, Paul described the law that we are not under as being a law were sin had dominion over us, so he was speaking about the law of sin, not about the Law of God. Moreover, in Romans 6:15, being under grace does not mean that we are permitted to sin, and in Romans 3:20, it is by the Mosaic Law that we have knowledge of what sin is, so we are still under it. In addition, everything else in Romans 6 speaks in favor of obedience to God and against sin.
In regard to Galatians 3:10-12, God is trustworthy, therefore His law is also trustworthy (Psalms 19:7), so the way to rely on God is by obedient relying on His instructions, it is contradictory to think that we should rely on God, but not on His instructions, and the position that God's instructions are untrustworthy/not of faith is the position that denies the trustworthiness/faithfulness of God. According to Galatians 3:10, the only way to avoid coming under the curse of the Law of God is by continuing to obey it, which is in accordance with what the passage that it is quoting from of Deuteronomy 27-28, where relying on God's law is the way to be blessed while not relying on it is the way to be cursed. So if someone were to rely on works of the law instead of relying on the Law of God, then they would thereby come under the curse for not relying on the Law of God. It would be absurd to interpret Galatians 3:10 as Paul quoting from a passage to support a point that is arguing against it by saying that relying on God's law is the way to be cursed and not relying on it is the way to be blessed.
In Galatians 3:10-12, Paul associated a quote from Habakkuk 2:4 saying that the righteous shall live by faith with a quote from Leviticus 18:5 that the one who obeys the Law of God will live by it, so the righteous who are living by faith are the same as those who are living in obedience to the Law of God. Moreover, the context of Habakkuk 2 contrasts the righteous who are living by faith with those who are not living in obedience to the Law of God and in Isaiah 51:7, the righteous are those on whose heart is the Law of God, so the righteous living by faith does not refer to a manner of living that is not in obedience to it.
In 1 Corinthians 9:21, Paul said in a parallel statement that he was not outside the Law of God, but under the Law of Christ, so he equated the Law of God with the Law of Christ, after all Christ is God, so Paul was denying that he was under the Law of God. Paul was speaking about giving up his rights in order to meet people where they were at, not speaking about doing what God's law reveals to be sin in order to reach sinners for Christ because that would have completely undermined his message.
In Romans 7:7, Paul said that the Law of God is not sinful, but is how we know what sin is, and when our sin is revealed, then that leads us to repent and causes sin to decrease. Furthermore, in Romans 7:12, he said the it is holy, righteous, and good, so it is a law where holiness, righteousness, and goodness have dominion over us. In contrast, the law of sin stirs up sinful passions in order to bear fruit unto death, so it is sinful, it causes sin to increase, and it is a law where sin has dominion over us. In Romans 6:14, Paul described the law that we are not under as being a law were sin had dominion over us, so he was speaking about the law of sin, not about the Law of God. Moreover, in Romans 6:15, being under grace does not mean that we are permitted to sin, and in Romans 3:20, it is by the Mosaic Law that we have knowledge of what sin is, so we are still under it. In addition, everything else in Romans 6 speaks in favor of obedience to God and against sin.
In regard to Galatians 3:10-12, God is trustworthy, therefore His law is also trustworthy (Psalms 19:7), so the way to rely on God is by obedient relying on His instructions, it is contradictory to think that we should rely on God, but not on His instructions, and the position that God's instructions are untrustworthy/not of faith is the position that denies the trustworthiness/faithfulness of God. According to Galatians 3:10, the only way to avoid coming under the curse of the Law of God is by continuing to obey it, which is in accordance with what the passage that it is quoting from of Deuteronomy 27-28, where relying on God's law is the way to be blessed while not relying on it is the way to be cursed. So if someone were to rely on works of the law instead of relying on the Law of God, then they would thereby come under the curse for not relying on the Law of God. It would be absurd to interpret Galatians 3:10 as Paul quoting from a passage to support a point that is arguing against it by saying that relying on God's law is the way to be cursed and not relying on it is the way to be blessed.
In Galatians 3:10-12, Paul associated a quote from Habakkuk 2:4 saying that the righteous shall live by faith with a quote from Leviticus 18:5 that the one who obeys the Law of God will live by it, so the righteous who are living by faith are the same as those who are living in obedience to the Law of God. Moreover, the context of Habakkuk 2 contrasts the righteous who are living by faith with those who are not living in obedience to the Law of God and in Isaiah 51:7, the righteous are those on whose heart is the Law of God, so the righteous living by faith does not refer to a manner of living that is not in obedience to it.
In 1 Corinthians 9:21, Paul said in a parallel statement that he was not outside the Law of God, but under the Law of Christ, so he equated the Law of God with the Law of Christ, after all Christ is God, so Paul was denying that he was under the Law of God. Paul was speaking about giving up his rights in order to meet people where they were at, not speaking about doing what God's law reveals to be sin in order to reach sinners for Christ because that would have completely undermined his message.
Here it is in the NET (with my emphases): Or do you not know, brothers and sisters (for I am speaking to those who know the law), that the law is lord over a person as long as he lives? For a married woman is bound by law to her husband as long as he lives, but if her husband dies, she is released from the law of the marriage. So then, if she is joined to another man while her husband is alive, she will be called an adulteress. But if her husband dies, she is free from that law, and if she is joined to another man, she is not an adulteress. So, my brothers and sisters, you also died to the law through the body of Christ, so that you could be joined to another, to the one who was raised from the dead, to bear fruit to God. For when we were in the flesh, the sinful desires, aroused by the law, were active in the members of our body to bear fruit for death. But now we have been released from the law, because we have died to what controlled us, so that we may serve in the new life of the Spirit and not under the old written code.
Nothing could be clearer. What can't you understand this basic principle of Christianity