Paul the apostle asserted that the gospel is centered on promise, while the Law is characterized by curse. Did he overstate the contrast? After all, there is an element of curse within the gospel, and there are promises within the Law.
Paul’s central claim, however, is that the gospel produces children of promise, in contrast to the children of the curse who live under the Law. The “children of promise” arise from the promise of the gospel Jesus revealed such as is recorded in John 8, which is freedom from the enslavement of sin to those who believe in Jesus and follow His teaching. This promise gives birth to true disciples; it is the causal factor of spiritual transformation. Those who seek righteousness through the Law are, in a sense, born of its curse—fearing failure to keep the Law: failure which brings a curse of condemnation. The “children of the Law” can still be like Satan, lying and murdering as he does. The Law is not enough to wholly prevent the various forms of murder and lying. In contrast, the “children of the gospel” can become children of God, because the promise of the gospel is sustained by the power, grace, and ministry of Jesus, who transforms believers and calls them to be saintly, no longer murderers and liars, or grievous sinners in other such ways. They believe that Jesus is the light of the world sent by God, trusting in him, and in holding to his teachings persistently, they experience the promised transforming spirit and truth, through the Holy Spirit’s workings, with power to make them children of God, not slaves of sin, nor children of Satan’s ways.