As indeed he says in Hosea, “Those who were not my people I will call ‘my people,’ and her who was not beloved I will call ‘beloved.’”  “And in the very place where it was said to them, ‘You are not my people,’ there they will be called ‘sons of the living God.’” (ESV)
When we read the words of the Apostle Paul we need to remember that we are listening to a Hebrew scholar. In Acts 22:3 we discover that Paul was educated under Gamaliel. For our understanding this would be like saying that someone had a prestigious degree from Harvard or Yale. Paul had been a "Pharisee of Pharisees." Paul's expertise in the Word brings him to quote the Prophet Hosea.
Hosea is a fascinating study in God's relationship with his people Israel. Hosea was asked by God to marry a prostitute and have children by her. In so doing, Hosea's relationship with his wayward wife would be a visual parallel to the relationship that God was having with Israel. God had been faithful to his covenant but Israel played the harlot, chasing after other gods.
As you understand the basic background of Hosea can you begin to see how God's words would be received? He is arousing jealousy in the heart of his beloved. Israel has chased after other gods. God is saying that he is offering his love and affection to other peoples. The incredible irony is that God is going to make a new covenant with people that Israel had been chasing after in her evil lust.
There is something else that is interesting to note here. God had always loved the Gentile peoples that will be called his people. Ephesians 1:4 tells us: "even as he chose us in him before the foundation of the world, that we should be holy and blameless before him." God loved the Gentiles and the Jews for all eternity. In Christ the new covenant with the Gentiles becomes a reality.
How is your relationship with God? Would he find you to be a faithful bride? Or are you chasing after things that would betray your relationship? Consider that we were chosen before the foundation of the world, that we should be holy and blameless before him.