Please read the passage before reading the commentary.
Two women, two mountains, two children, one slave and one free. Generally, when a female slave has a child, the child is a slave even if the father is a freeman. It was so in the United States with slaves as it was true in ancient times. Hagar was the slave of Sarah; Isaac was the son of Sarah. Sarah was very old, well past the age for bearing children, had been promised a son in her old age. Ishmael was the son of Hagar, and therefore a slave; Isaac was the son promised to Sarah and was therefore free. Mt Sinai is not in the Promised land; Jerusalem, even as the New Jerusalem, was on a mountain in the Promised Land. The Gentiles, spiritually, are the children of Hagar; the believers in Jesus are spiritually the children of Sarah. The slaves, called Gentile here, want to bind Christians to the law, which was given on Mt Sinai. Paul argues that the freeborn Christian Galatians have the freedom Christ has won for them.
The two women represent two covenants, one not from the Promised Land and the other from Jerusalem. Paul cites Isaiah 54, 1 to show that the once-barren Sarah will have more Christian children than the pro-circumcision non-Christians have.
The Galatians had accepted the freedom that Christ gives. Paul, then, encouraged them not to submit to the yoke of slavery again. We, like the Galatians, have received the freedom Christ gives through his Spirit. We, like the Galatians of old, have begun in the Spirit and should beware not to return to the old ways of living according to Gentile standards of sin. Sin is slavery that leads to death, Christ is freedom that leads to life.