Gen 21- Ishmael and Isaac

After listening to seven hours of sermons from four different teachers, the best lesson I can grasp concerning the split in Abraham's lineage between Isaac and Ishmael simply comes directly from our Apostle Paul in Galatians 4-

Tell me, you who desire to be under the law,

do you not listen to the law?

For it is written that Abraham had two sons,

one by a slave woman and one by a free woman.

But the son of the slave was born according to the flesh,

while the son of the free woman was born through promise.

Now this may be interpreted allegorically:

these women are two covenants.

One is from Mount Sinai,

bearing children for slavery;

she is Hagar.

Now Hagar is Mount Sinai in Arabia;

she corresponds to the present Jerusalem,

for she is in slavery with her children.

But the Jerusalem above is free,

and she is our mother.

For it is written,

“Rejoice, O barren one who does not bear;

break forth and cry aloud, you who are not in labor!

For the children of the desolate one will be more

than those of the one who has a husband.”

Now you, brothers, like Isaac, are children of promise.

But just as at that time he who was born according to the flesh

persecuted him who was born according to the Spirit, so also it is now.

But what does the Scripture say?

“Cast out the slave woman and her son,

for the son of the slave woman shall not

inherit with the son of the free woman.”

So, brothers, we are not children of the slave

but of the free woman. -Galatians 4:21-31