Christ took his disciples to the outskirts of Jewish culture and influence (15:21). They met others in need (including this "foreigner) who was treated by the disciples and others as no better than dogs (15:23). It appears that Christ sensed that if given half a chance this woman would continue to follow Him (15:26). He then showed to the disciples that the Good News was not just for a select few, but for everyone.(Luke 9:55,Acts 1:8) He used their own bigotry to show them the contrast of God's love for ALL people. They weren't ready for it then, but learned to understand later on. (Acts 10 & 11; Acts 11:18)