Just had another debate with the Pharisees about uncleanness. Now he encounters a Gentile woman who needs her demon-possessed daughter healed. The Jewish people considered non-Jewish people to be "dogs". Dogs were not the beloved pets that they are now. They were dirty scavengers to be avoided. That is how the Jews saw non-Jews.
And Jesus himself truly did come to Israel first because that was his first nation called under his name. Although his message was to all kinds of people, he first wanted his nation to hear it while he walked the earth. This is why when the woman comes, he essentially calls her a dog. But either he says it with a warm smile on his face or she is desperate enough to see her daughter healed. She keeps asking and says that even the dogs are getting the crumbs from the main table. Jesus is focusing on just the Jews, but the rest of the world is watching and getting some of the message. Jesus gladly heals her.
He then goes on to heal the deaf and dumb man from the same region near Phoenicia and he feeds 4000 people who are mostly Gentile. Just like with the 5000, the disciples forgot what Jesus could do, but he still graciously multiplied his bread so that all could eat. Then, Jesus and his disciples go sailing along and Jesus says do beware the leaven of the Pharisees. The duh-sciples, as they are called by us (which is unfair because we make the same mistakes), still thought he was talking about them forgetting about the bread. No, Jesus was warning them not to be so self-satisfied. God chose Israel as his nation and he chose all believers as his people, but he did not have to do so. His grace is a gift and not earned. He forgives sin because he wants to. He is a savior by nature. We must extend the same grace to all people.