John Chrysostom
With the intent of humbling the pride of Hagar, she compelled her to leave in great anger, as noted in Genesis 16:4-6. Now, desiring to address the arrogance of Ishmael from the outset and unable to tolerate the notion that a son conceived in grace, destined by God, should be treated alike with the son of an Egyptian bondwoman, she instructed Abraham to expel this slave woman and her son. She declared that the son of the bondwoman would not share in the inheritance with her son Isaac. Aware of her advanced age and that her forefather was also aging, having lived many years, Sarah feared that upon their unforeseen deaths, Ishmael, by virtue of his birthright from the lineage of the forefather, might stake a claim to his father's inheritance and vie for a position equal to that of Isaac.
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Hence, she asserted the need to send away this bondwoman and her son, indicating that the son of the maidservant should not have any association with her son Isaac, nor should it be appropriate for the son of the maidservant to engage closely with the son of his mistress.