Paul's argument against the law is stepped in the practices of the Christians at the time which from Acts, Peter had already started converting Gentiles and arguing against some things considered unclean (in this case food and gentiles).

And by the time of Galatians, many of the Gentile converts weren't even circumcized but still mostly accepted in the Christian community.

Galatians is Paul laying the argument that Gentiles don't have to become Jews to be Christians.

He makes the argument that since the Law is revelation and was mediated through Angels, it lacks the Full Agency of God, thus Jesus who is considered Fully Man and God has that Full Agency and that Jesus statement that the Law is summarized in Loving God and loving man is the true agency of God.

The way the law was given in the Old Testament is either just before or just after the Jews break a Law so in Galatians 3:19 he argues that the law was revealed to mitigate against these transgressions. Thus the Law was given to serve the good of the Jews but at the place (Canaan) and Time (judges, prophets and kings era) and serves a purpose in the final fulfilment of God's promise to Abraham. Thus he argues it is temporary and serves an intermediate purpose.

Christ is this fulfilment of the law (Matthew 5:17) and the fulfilment of God's plan.

But at the same time the law is still considered good (it was still given by God, even if not the finality) and considered more of a guide now than exacts. Tho Paul never resolves how exactly the law is supposed to function as subservient to Christ in the lives of Christians.

So this is basically Paul's argument on how the Old Testament can be inspired by God but not the eternal law for all time.

But the Traditional churches (Catholic, Orthodox and Eastern), consider this to be the duty of the Church to decide how exactly the Old Testament law intersects with the New Testament.

The Protestants however seem to be divided into 3 rough camps of just follow the love commandment (Quakers and most Liberal Theology people are here).

Follow every law except those explicitly ended by the New Testament (Lutherans) and trusted revelations (Charismatics)

Follow the laws that the New Testament repeats (most non-denominationals)

Some support for this. For one Jeremiah talks about God interfering with the hearts of the Isrelites so that following the law becomes their new nature and not just following a rule book.

Jesus argues against the Pharisee about the divorce law, saying that the law given to the Isrealites was a compromise as their ancestors would never even hope to follow the perfect law and were given a sort of reduced law moulded to their nature. Matthew 19:3-12.

Also the ripping of the veil of the holy of holies at their death of Christ, removing the symbolic distinction between the holiest and most mundane spaces.

Jesus calls himself the Fulfilment of the Law.

The support from the revelations to Peter in Acts 10, where he is commanded to eat of ritually unclean animals, and his actions soon after to convert ritually unclean people (uncircumcised Gentiles) and in Galatians 1&2, to associate, eat with and promote within the church of uncircumcised Gentiles.

There is a certain theme among these Laws that Peter has been commanded to disregard and that is the ritual nature of all of these laws, laws whose purpose had been to remove and/or protect from uncleanliness.

Following from the ripping of the distinguishing veil, the fact that Cyrus who could not have followed these ritual laws was still considered righteous by the later prophets like Nahum, the idea that it is laws specifically dealing with uncleanliness and not sin that are specifically abrogated is present in many Christian sects, Traditional and Protestant.

So this is a condensation of Paul's message concerning the Law in Galatians as well as how the different denominations deal with the ambiguities.