Paul gives two interesting analogies in this passage. The first analogy starts by explaining how young children who have an inheritance waiting for them after their father dies are actually not much different than slaves. While the inheritance is in their name, they don't have access to do whatever they want with it because they don't yet have the maturity to deal with it. Instead, they depend on their guardians to help step in the place of their parents to provide for their needs, but the full inheritance is not given until they are of mature age. In a similar way, God's people were subjects and slaves to the law until Jesus himself came to fulfill the law and buy us our freedom. The difference is that instead of God just becoming our guardian, he steps in as our adopted Father as if we were His own. And as one of his children, not only are we not slaves, we receive an inheritance of infinite value that is already given to us.

The second analogy is also related to our relationship to the law vs freedom. Abraham had two wives who each had sons, but one (Ishmael born to Hagar) was born into slavery, while the other (Isaac born to Sarah) was born into freedom. Just the same way Mt Sinai was the location the people of Israel were brought the law and being made subject to it, also the heavenly Jerusalem represents the freedom God intended for us. Again, because of the sacrifice of Jesus we have the privilege and honor of being born directly into freedom, becoming adopted children of the Father and receiving an inheritance as one of his own children.