Or HaChaim on Genesis 21:24/אור החיים על בראשית כ״א:כ״ד

1 ויאמר אברהם אנכי אשבע. Abraham said: "I will swear." Abraham implied that he could counter Avimelech's arguments but had decided instead to swear as Avimelech requested.

2In consideration of Abraham's intention to rebuke Avimelech (verse 25), he thought that if he did this immediately Avimelech would interpret Abraham's attitude as a denial of the favours the king claimed to have done for him. He decided therefore to state first of all that he was willing to swear the oath in question.

3Another way of looking at the verse is that Abraham accepted the oath only for himself, i.e. אנכי; he was not prepared to commit his son or grandson as had been requested by Avimelech.