Why does Paul use inclusive language for Jew and Gentile in Galatians 4:5?
Paul includes Jew and Gentile because Christ's redemption did not stop with Israel but spread to the whole human race, and Paul was writing to Gentiles. The purpose is that both might receive adoption as sons, which could never happen without the price of redemption paid at the cross.
Les explains that in Galatians 4:5 Paul first says Christ came, made of the woman, to be King of Israel; when Israel rejected that, His eternal purpose was to go to the cross, shed His blood, and pay the full price of redemption. That redemption first applied to those under the law—Israel—but it did not stop with Israel. It spread to the whole human race. So Paul uses terminology including everybody, Jew and Gentile, because he is writing to Gentiles, so that “we” might receive the adoption of sons. That adoption could never happen without the price of redemption, which had to be one of the first processes in the plan of salvation. In Romans 3, Paul likewise says God is both just and the justifier of him who believes.
To redeem them that were under the law, that we might receive the adoption of sons.