The lesson God has for us in Galatians 4:19-31 is that we cannot ever fulfill the commandments of God by our own human efforts. They can be kept only as we accept Christ as Saviour.
Then, through the indwelling Spirit, the life of Christ is fulfilled in us.
The bringing of Ishmael into the world was all of man's planning. God had nothing to do with it. That which is of the flesh displeases God, and He will not accept it.
Ishmael was a child born after the flesh; and since his mother was a slave, he, too, was a slave.
With Isaac it was entirely different. He was born of a freewoman. His coming into the world was due to God's work.
So the point made here is that we are considered through faith in Christ to be the brethren of Isaac. We are the children of promise, born through divine power and not through human effort.
There is a strong tendency on the part of those who insist that Law is necessary for salvation to persecute those who preach salvation by grace plus nothing. Those who insist on Law say that we who preach grace are making it easier for people to sin.
But this is not the case. Grace does not give people license to sin. It teaches us to deny ungodliness and worldly lusts and to live soberly and righteously in this world. So even though opposition or even persecution comes, we should be ready to endure it.
But what is to be our attitude in this teaching of Law and grace? Are we to go along with the teachers of Law and say nothing?
The answer of Scripture is, "Cast out the bondwoman and her son: for the son of the bondwoman shall not be heir to the son of the freewoman" (v. 30). The two will not mix. We are saved by grace. We are not in bondage to the Law. We cast it from us.
"Stand fast therefore in the liberty wherewith Christ hath made us free, and be not entangled again with the yoke of bondage" (Gal. 5:1).