In this verse, Paul draws a parallel between believers and Isaac, the son of Abraham and Sarah, who was born as a result of God's promise. Isaac's birth was miraculous and fulfilled God's promise to Abraham, symbolizing the fulfillment of God's word despite human limitations. Similarly, Christians are considered 'children of promise' because they are born into God's family through faith in Jesus Christ, not through human effort or adherence to the law.
This analogy serves to remind believers of their spiritual heritage and the assurance that comes with being part of God's covenant. It underscores the idea that faith is the means by which they inherit God's promises, just as Isaac inherited the blessings promised to Abraham. This identity as children of promise brings with it a sense of belonging and purpose, encouraging believers to live in the freedom and joy that comes from being part of God's family. It reassures them of their place in God's eternal plan, emphasizing that their relationship with God is based on His grace and promise rather than their own works.