What is the church? Children of the promise.

What is the church?  And what can we liken it to in Genesis 21?

"And Yahweh visited Sarah as he had said. And Yahweh did to Sarah as he had promised. And she conceived, and Sarah bore to Abraham a son in his old age at the appointed time that God had told him."  

"And Sarah saw the son of Hagar the Egyptian, whom she had borne Abraham, mocking. Then she said to Abraham, “Drive out this slave woman and her son, for the son of this slave woman will not be heir with my son, with Isaac.” And the matter displeased Abraham very much on account of his son. Then God said to Abraham, “Do not be displeased on account of the boy and on account of the slave woman. Listen to everything that Sarah said to you, for through Isaac your offspring will be named...."

"Then Jesus said to those Jews who had believed him, “If you continue in my word you are truly my disciples, and you will know the truth, and the truth will set you free.” They replied to him, “We are descendants of Abraham and have not been enslaved to anyone at any time. How do you say, ‘You will become free’?” Jesus replied to them, “Truly, truly I say to you, that everyone who commits sin is a slave of sin. And the slave does not remain in the household forever; the son remains forever. So if the son sets you free, you will be truly free."  John 8

"Tell me, you who are wanting to be under the law, do you not understand the law? For it is written that Abraham had two sons, one by the female slave and one by the free woman. But the one by the female slave was born according to human descent, and the one by the free woman through the promise, which things are spoken allegorically, for these women are two covenants, one from Mount Sinai, bearing children for slavery, who is Hagar. Now Hagar is Mount Sinai in Arabia, and corresponds to the present Jerusalem, for she is a slave with her children. But the Jerusalem above is free, which is our mother. For it is written,

“Rejoice, O barren woman, who does not give birth to children;
    burst out and shout, you who do not have birth pains,
because many are the children of the desolate woman,
    even more than those of the one who has a husband.”

But you, brothers, are children of the promise, just as Isaac. But just as at that time the child born according to human descent persecuted the child born according to the Spirit, so also now. But what does the scripture say? “Drive out the female slave and her son, for the son of the female slave will never inherit with the son” of the free woman. Therefore, brothers, we are not children of the female slave but of the free woman."  Gal 4