This post follows the Bible reading plan available at oaktreechurch.com/soap. You can read all my New Testament notes in my book New Testament: Chapter by Chapter.
Chapter four continues the second section of the letter and the explanation of the inheritance available to all who believe in Jesus. Galatians 4:1-7 contains the wonderful truth that Jesus was born at just the right time in just the right manner to accomplish everything God wanted to do, namely, to adopt rebel humans back into his spiritual family and make us free. This is important because we are all enslaved in sin by nature (Galatians 4:8-12; Ephesians 2:1-3), but in Christ we are freed from that. Paul wondered, then, why someone would place himself under any kind of restrictions again.
Galatians 4:13-20 breaks from Paul’s explanation of his doctrine to a personal appeal to his original readers. He reminded them of how they had received him. Even though he was violently ill, they were not repulsed by him, but rather received him and his message as if he were Jesus himself. In fact, Paul noted that they would have gouged out their own eyes and given them to him if they were able. 1
This chapter (and the second section) closes with an allegory (an extended metaphor), in which Paul likened the old covenant to Hagar and Ishmael.