What is the reason for Yishmael's expulsion? Why did God agree to Sarah's demand? Numerous responses have been proposed, ranging from sinful behavior on the part of Yishmael, to the currently popular metaphysical doctrine that the chosen nation can be formed only through the process of "choosing," the pushing aside or purging of one of two possible heirs.
In analyzing the details of the third part of the chapter, the "Expulsion of Yishmael," treating it as a "Journey, Danger and Rescue" story and contrasting it with another such story of that type, "Akeidat Yitzchak," a new explanation for God's acquiescence becomes apparent.
Unlike us, the readers of the Bible, or even Avraham and Sarah, God knows the future. God knows the character and capabilities of Avraham and Hagar, of Yitzchak and Yishmael. God knows how Avraham and Yitzchak will react to the Akeida, to the ordeal of "Journey, Danger and Rescue." He already apprehends their capacities for faith, courage, purposefulness and togetherness. He knows they are cut from a certain cloth. Likewise, he knows the essence of Hagar and her son Yishmael. He knows how they will respond to their comparatively mild trial of faith, their journey and danger. He knows that despair, division and breakdown are not the best materials from which to mold the nation of Avraham. Consequently, just as God first chose the long-suffering Sarah and her child Yitzchak in the covenant of circumcision, so too God chooses Sarah and her child Yitzchak here in Chapter Twenty-One.
To close the circle, the details of the "Expulsion of Yishmael" and the implied contrast to Akeidat Yitzchak are about letting us, the readers, in on these insights. By reading on, grasping what the character of faith is about and grasping what it is not about, we may also have begun to grasp the rationale for God's decision.