Why are Christians called children of the promise?

In Romans 9:7–9, it becomes abundantly clear that the true children of Abraham, the Israel of God, are united into one body solely through faith in God and in his promises. Those who lack this faith are excluded. God’s Israel is not constituted by race, but by faith. It is not the genes, but the promises that bind us together. God actually already established this principle when Israel was but a child when he said: Through Isaac shall your offspring be named (Romans 9:7b). These words were spoken to Abraham when God told him to send away Hagar and their son Ishmael. Abraham had two children, Ishmael and Isaac, and yet the promise only applied to a child of Abraham and Sarah. As such Isaac stayed—not because Ishmael was inferior, but because, from the outset, it had to be clear that it is only by means of the promise (and faith in that promise) that God’s people could be constituted. Paul describes this clearly: This means that it is not the children of the flesh who are the children of God, but rather the children of the promise that are counted as offspring (Romans 9:8). For Christians of later centuries this might seem rather obvious, even if it still causes some tension in our discussions with Muslims. On the one hand it does deprive the offspring of Ishmael from the obvious right to call themselves the people of Abraham, but on the other hand, by faith in God’s promises, they too can obtain the same rights as the descendants of Isaac, who themselves do not possess any inherent birth rights either.

But just in case this is still not entirely clear to the readers, Paul provides yet another explanation of what exactly he means by the promise in Romans 9:9: For this is what the promise said: About this time next year I will return, and Sarah shall have a son. Isaac's birth itself was the fulfillment of a divine promise (Romans 4:17–21), for when Abraham and Sarah had reached a very advanced age, they only had the word of promise that called into existence that which did not exist. Paul therefore does not merely intend to convey that there was already a promise for Isaac as Israel’s founding father, but rather that his entire existence was due to God’s promise to his parents. God created a people by his creative word in a seemingly hopeless situation wherein (as far as nature was concerned) no child could be born anymore, let alone a people be birthed.¹