Read Part 1.
What do we make of the reference to being “born of a woman” in Galatians 4:4c? Christologically, I have no qualms with Christians bringing to mind the incarnation—Jesus as deity and man, fully. I don’t know that this was Paul’s intention though (again, even if it isn’t, that doesn’t mean it can’t inform a Christian’s thinking about Jesus). It could be that Paul has Genesis 3:15 in view. The seed of woman will severely bruise the head of the serpent and the serpent will severely bruise the heel of the seed of woman. Jesus is that one born of the woman, Mary, the new Eve. Again, this might be anachronistic. It is hard to know how developed these thoughts were in Paul’s mind, but it no surprise to me that the church has heard these themes in Paul’s words over the years.
As to being “born under the Law” I think this brings us back to Galatians 4:4a—“when the fullness of the time came” or when the time of the Law’s reign over the children of God was in effect, messiah arrived. Paul says that Jesus redeemed those who were “under Law” (ὑπὸ νόμον, v. 5) and I am inclined to think that this is a more precise reference to Israel, those who had been given the Law (e.g., Romans 9:4). Messiah comes under the Law to deliver those under the Law. This is how he brings Israel into full sonship as well as all those who were not Israel, but the “nations” that Paul saw as being promised to Abraham. The Spirit adopts us fully and now we can call God, “Abba! Father!” (Gal. 4:6). Those under the Law receive full adoption. Those who did not know God, but worshipped things that are “no gods” (μὴ οὖσι θεοῖς, v. 8), know God now (v. 9).