Genesis 21:1-21
God’s promise is being fulfilled. "At the set time" Isaac is born. He is a picture of Christ in His character as Son and Heir (Hebrews 1:2). After the incredulous laughter of Abraham (Genesis 17:17) and Sarah (Genesis 18:12), then Sarah’s joyful and thankful laughter, the very meaning of the name Isaac (laughter), (vv. 3, 6), we then hear the mocking laughter of Ishmael (v. 9). He is a figure of man "after the flesh" who can understand nothing of the counsels of God fulfilled in Christ. Ishmael, the son of the servant, is a picture of man under the bondage of the law, who has no right to the promises or to the inheritance.
What Sarah then does seems hard; Abraham finds it "grievous". But God approves of it because He wants to demonstrate by it, figuratively, that the inheritance belongs to Christ alone and that, by works, man does not possess any part of it. As the epistle to the Galatians explains, believers are "children of promise". Having received the adoption, they are no longer servants but sons and therefore heirs (Galatians 4:6-7; ; Galatians 4:28).
Nevertheless grace moves towards Hagar and her son. When the water in the goatskin bottle, which is a symbol of human resources, is exhausted, the living God, who had revealed Himself to her in chapter 16, renews her deliverance. He is the One who hears the voice even of a child (v. 17).