In Galatians 4:21-31 Paul shares that God pours out grace not to those who are attempting faultless obedience to the law (which is impossible), instead His grace is showered on those who rely solely upon what Jesus did at Calvary. Adding anything to the cross of Christ is like pouring raw sewage into pristine water; it contaminates it.
Now the Jews loved boasting that they were Abraham’s children and so they taught that Gentile believers should add obedience to the Law to their faith in Christ, so they could be Abraham’s children too. Paul wisely points out that Abraham had two sons; Ishmael and Isaac.
Ishmael, born from the slave woman through man’s schemes represents those who reject the eternal sufficiency of Christ’s sacrifice and who instead seek salvation through works of the Law; for them Christ’s atoning sacrifice was insufficient. The impossible works of obeying the Law brought bondage and misery. But Isaac, born from the free woman through God’s promise, represents those who wholly trust in Christ’s blood for their salvation, which ushers in freedom and joy.
Though Hagar was fertile, her pregnancy was man’s idea and ultimately brought suffering, but Sarah though barren, conceived Isaac through divine promise and intervention. This brought not only joy and laughter (Isaac’s name means laughter), this barren woman also became the mother of innumerable children who would receive God’s grace through believing God’s promises as Abraham had and through Christ we are all Abraham’s children and thereby heirs of God’s blessings!