John Calvin Commentary Genesis 21:9

"And Sarah saw the son of Hagar the Egyptian, whom she had borne unto Abraham, mocking." — Genesis 21:9 (ASV)

And Sarah saw the son of Hagar. As the verb "to laugh" has a twofold meaning in Latin, so also the Hebrews use, in both a good and evil sense, the verb from which the participle מצחק (metsachaik) is derived. That it was not a childish and harmless laughter is apparent from Sarah's indignation.

It was, therefore, a malignant expression of scorn, by which the insolent youth manifested his contempt for his infant brother. And it should be noted that the epithet applied here to Ishmael, and the name Isaac, are both derived from the same root. Isaac was, to his father and others, the occasion of holy and lawful laughter, from which also the name was divinely given to him.

Ishmael turns the blessing of God, from which such joy flowed, into ridicule. Therefore, as an impious mocker, he stands opposed to his brother Isaac. Both (so to speak) are the sons of laughter, but in a very different sense. Isaac brought laughter with him from his mother’s womb, since he bore—engraved upon him—the certain sign of God’s grace.

Isaac therefore fills his father’s house with such joy that joy breaks forth in thanksgiving; but Ishmael, with canine and profane laughter, attempts to destroy that holy joy of faith.

And there is no doubt that his clear impiety against God revealed itself in this ridicule. He had reached an age where he could not possibly be ignorant of the promised favor, for which his father Abraham was filled with such great joy; and yet—proudly confident in himself—he insults, in his brother, both God and His word, and the faith of Abraham.

Therefore, it was not without cause that Sarah was so vehemently angry with him that she commanded him to be driven into exile. For nothing is more grievous to a holy mind than to see the grace of God exposed to ridicule. And this is the reason Paul calls his laughter persecution, saying:

He who was after the flesh persecuted the spiritual seed. (Galatians 4:29)

Was it with sword or violence? No, but with the scorn of the virulent tongue, which does not injure the body but pierces the very soul. Moses might indeed have emphasized his crime with many words, but I think that he intentionally spoke so concisely to make the insolence with which Ishmael ridicules the word of God more detestable.