Righteousness Based on the Law (Lev 18:5; Ezek 20:11; Gal 3:12; Rom 10:5)
If Paul had ever taught that the law could never give life, then he is a false prophet for making God a liar, and it also implies that all Patriarchs went to hell by obeying God in vain. Surely, it makes God a liar if we can imagine that the law could never justify despite the repeated promise of God. This idea that the law was contrary to promise or was useless is the most abhorrent to Paul (May it never be, or God forbid). See my answer Christianity-SE: Was eternal life promised by the law of Moses? The law was called the book of life, not for a prolonged temporary and vain earthly lifetime which the pagans aim for, but the eternal life in heaven. The prosperous life of Israelites was a consequence of obeying God as a nation for the national covenant to demonstrate God's work to the world, and make them envious. Jesus also answered the young ruler, on his question on eternal life, that obeying God obtains eternal life. Here, I will focus on the immediate context of Paul.
Paul was not a false prophet who insulted the law of Moses given by God. It is a myth that he taught the law was a deception of God, or worthless in its promise based on lawless antinomian theology with illogical assumptions like nobody could ever keep the law when we know there were countless perfect men found in the scripture. He warned the Galatians against circumcision saying if you accept circumcision, you're not mere taking just one thing from the law, you'd be bound to the whole law. It never implied that he warned them because obedience is impossible, but because now it is impractical since the law has been nullified; and it is mutually exclusive to the new covenant of Promise. Jesus said in Matt 9:12-13 that he came for the sick, not the healthy, the healthy don't need the doctor, but the detractors would turn that into sarcasm as well. Paul's arguments were clear that now righteousness does not come by the law after the new covenant of Christ, the law of justification has changed. No one is justified by the law of Moses anymore. His arguments about the nullification of the law are only in the present tense, due to the arrival of the promise. A righteousness apart from the Mosaic law.
[ESV Romans 3:21-22] But now the righteousness of God has
been manifested apart from the law, although the Law and the Prophets
bear witness to it— the righteousness of God through faith
in Jesus Christ for all who believe.
[ESV Galatians 3:18-19] 18 For if the inheritance comes by
the law, it no longer comes by promise; but God gave it to Abraham
by a promise. 19 Why then the law? It was added because of
transgressions, until the offspring should come to whom the
promise had been made, and it was put in place through angels by an
intermediary.
This is the new requirement for righteousness apart from the law based righteousness. So how come someone can interpret that there was never any law based righteousness to begin with? The righteousness according to God's criteria has changed. Those who rejected Christ are trying to establish their own righteousness criteria, which is rebellious to God's law/requirement. If you understand "until" and "no more/no longer" then the context should be evident that Paul is only writing about the present fact of change of the righteousness criteria. Change of covenant (Heb 7:12).
In Romans 7, he also explains with the example of the marriage, that she is no longer under the covenant after the death of her husband, cf. Heb 9:15-16. Christ has nullified and ended the law based righteousness, his requirement for righteousness is easier by grace. If there was never a righteousness of the law, then how could Christ have been the end of it?
[ESV Romans 10:3-5] 3 For, being ignorant of the
righteousness of God, and seeking to establish their own, they did not
submit to God's righteousness. 4 For Christ is the end of
the law for righteousness to everyone who believes. 5 For
Moses writes about the righteousness that is based on the law, that
the person who does the commandments shall live by them.
Galatians 3:21b "If a law had been given": the worst mistranslation
Yes, the law had been able to give life (see Ps 119), but not anymore, otherwise it would be contrary to the promise. Paul never writes that we are innately sinners and cannot keep the law, but even some Gentiles keep the law and will be justified as righteous (Rom 2:6-12) just as Christ said about the good Samaritan (Luke 10). If Paul argued that man cannot keep the law due to his inability and corruption, then neither can he keep the law of Christ, and God wouldn't have given the law to the patriarchs while deceiving. Can God make us able to keep the new law, but couldn't make the saints of the old?
This false translation issue should be the most controversial, as the whole protestant theology hinges upon it. I have made a question on Galatians 3:21 translation issue seeking for the clarifications & analysis on the reading "if a law had been given that could give life" εἰ γὰρ ἐδόθη νόμος ὁ δυνάμενος ζῳοποιῆσαι. This reading suggests that no law was (ever, had been) given that could give life. Such a translation go absolutely against the repeated plain harmony of the context. It should rather be "If the law that was given could give life", as just a few translations put it to my knowledge (NJB, GWT, Godbey, NLT and Wycliffe).
Galatians 3:21b
(New Living Translation)
If the law could give us new life, we could be made right with God by obeying it.
(Wycliffe) For if the lawe were youun, that myyte quikene, verili
were riytfulnesse of lawe.
(New Jerusalem Bible)
If the Law that was given had been capable of
giving life, then certainly saving justice would have come from the
Law.
(English Standard Version) For if a law had been given that could give
life, then righteousness would indeed be by the law.
It should be "If the law that was given" or "the given law", at worst, "If the law had been a law capable of giving life" (Jamieson-Fausset-Brown commentary)
Some other commentators have also explained that the question is not whether such a law was given, but whether the given law could give life. Their interpretation of the verse is correct, despite the fact that none has objected to the translation and hold to the traditional Lutheran theology. The existence of the alternative translations that I support show that at least it is a possible translation.
Bengel's Gnomen The conditional force does not fall upon was given, for the law was certainly given, but upon was able (could
have).—ὁ δυνάμενος, that was able) The article shows that the emphasis
is on δύναμαι.
Pulpit commentary ..The construction of the article in the phrase, νόμος ὁ δυνάμενος, is similar to that in ἔθνη τὰ μὴ ἔχοντα
(Romans 2:14); μάρτυσι τοῖς προκεχειροτονημένοις (Acts 10:41). The
noun is first put undetermined, a narrowing determination with the
article being then added: "If [in the Law of Moses] had been given a
Law such as," etc. By fastening attention upon the Law as unable "to
make alive," the apostle marks its character as contrasted with the
new covenant.
The argument of 3:21 is exactly as 2:21
[ESV Galatians 2:21] I do not nullify the grace of God, for if
righteousness were through the law, then Christ died for no purpose.
So, even if my objection is wrong, at worst it can be permitted to translate "If [it i.e. the law] gave a law (as in principle) that could give life." Such a statement seems unnatural, nonetheless it doesn't imply the readings that forces a specific interpretation. The force is on able not on given. The translators don't even provide an alternate reading in footnotes, to come across as objective. There is no sense of "had been" when he is talking of present facts of changing of the law/covenant. The mistranslation of Gal 3:21 is solely based on deliberate theological bias. Its interpretation has no connection with the Jewish theology of the Bible. If someone can add to the translation analysis and information on this verse from commentators, teachers or anyone then please post an answer to my question, to add to my research as I don't read Greek.
Related: Is it appropriate to translate Galatians 3:21 as "If a law had been given"?