Genesis 21 is the story of Isaac's miraculous birth and the sending away of Ishmael and his mom, Hagar. Casting them out might seem cold and harsh but it is absolutely crucial for us to do. Paul in Galatians 4 allegorizes this story. He says it stands for a spiritual reality going on inside us. Isaac and Ishmael are in us. They are fighting. You know what I mean. Just read Romans 7.
Before you're saved you were fairly content. You didn't think about your soul that much. After you're saved it seems you have a battle. The old nature while defeated is still there and raises up its ugly head. We can overcome it. Ephesians 4: 22-24: " You were taught, with regard to your former way of life, to put off your old self, which is being corrupted by its deceitful desires: to be made new in the attitude of your minds: and to put on the new self, created to be like God in true righteousness and holiness."