Albert Barnes Commentary Galatians 4:23

"Howbeit the [son] by the handmaid is born after the flesh; but the [son] by the freewoman [is born] through promise." — Galatians 4:23 (ASV)

But he who was of the bond-woman was born after the flesh. This occurred in the ordinary course of nature, without any special promise or any unusual divine intervention, as in Isaac's case.

But he of the free-woman, etc. Isaac's birth was in accordance with a special promise and by a remarkable divine intervention (Genesis 21:1–2; Hebrews 11:11–12).

Compare. See Barnes on Romans 4:19-21.

Paul's idea here is that the son of the slave was in a humble and inferior condition from his very birth. No special promise accompanied him. He was born into a state of inferiority and servitude, which accompanied him throughout his life.

Isaac, however, received promises as soon as he was born and benefited from those promises as long as he lived. Paul's object is to state the truth regarding a condition of servitude and slavery: it is accompanied by evils from beginning to end, from birth to the grave.

By this illustration, he means to show them the folly of becoming voluntary slaves to the law after they had once been set free (see Romans 9:7-8 regarding the "bond woman").