In these verses, Paul illustrates his message with a symbolic allegory, based Abraham's 2 sons, (1) Ishmael and (2) Isaac, born from 2 different mothers, (1) Hagar (the slave) and (2) Sarah (the free woman). The 2 sons derived their nature and status from their mothers, either (1) slavery (bondage) or (2) freedom. These 2 mothers represent (1) the Old Covenant (Law) associated with Mount Sinai, and (2) the New Covenant (Grace), associated with Mount Zion, the heavenly Jerusalem. (1) Just as Ishmael's birth was according to the flesh, by human initiative and effort (Genesis 16), so the children of the law are the product of their own effort and works. (2) Just as Isaac's birth was supernatural, through receiving God's promise (Genesis 17), so the children of the promise (Gospel) are born of the Spirit, the product of God's grace.

We make a special study of God's supernatural work of grace by God's Spirit in bringing Isaac to birth, when Abram and Sarai believed His Word (promise), a picture of our supernatural New Birth by God's Spirit, when we believed His promise through the Gospel. Whereas (1) Ishmael, the man of the flesh, was cast out, (2) Isaac, the man born of the Spirit by grace, inherited the covenant, including the blessing of eternal life.
Every person is either (1) an Ishmael, or (2) an Isaac. Who is your Mother?