Or HaChaim on Genesis 21:11/אור החיים על בראשית כ״א:י״א

1 על אודות בנו. On account of his son. Abraham was afraid that the expulsion would result in Ishmael pursuing unwholesome activities because he felt rejected. He had to be concerned about this since Ishmael was his son after all.

2Another meaning of this expression is that Abraham resented Sarah's describing Ishmael as merely "the son of this slave-woman." G'd now interfered by telling him that Sarah was entirely justified. When G'd pointedly referred to Ishmael as הנער, the lad, and not as "your son," He made it plain that only Isaac would be considered an extension of Abraham. G'd added: "also the son of this slave-woman," when He referred to Ishmael as having a major role in history. When the Torah describes Abraham as complying with Sarah's i.e. G'd's request, he no longer refers to Ishmael as "his son," but only as "the child."