O woman, great is your faith! Jesus uttered these words after initially reacting to the woman’s requests with what can be considered somewhat rude, if not derogatory, statements. The woman, of Canaanite origin and thus a pagan, approached Jesus with a request to have him come with her and attend to her daughter who was in need of healing. So much determined was this woman that neither the first nor the second "rude" response by Jesus could discourage her. As pagan as she was, she recognized Jesus' authority and power to grant her daughter the salvation that she desperately needed. But why would Jesus who had so far presented himself as a lover of the outcast and the alien be so rude to her? 
I tend to believe that our answer is found in the preceding pericopes. At the end of chapter 13, Jesus laments at the lack of faith among his own kin, something which led to Jesus not working any miracles in their midst (cf. Matthew 13: 53ff). Immediately preceding the episode about which we read in today's Gospel passage, we find Peter almost sinking because he allowed doubt to blur his faith. In contrast to these, a total stranger exhibits a kind of faith that is lacking in the other two scenarios. She becomes a model of what a disciple should be, a model of what kind of faith a disciple should have. Unlike the people of Nazareth, she did not have the advantage of belonging to the elected race; unlike Peter, she did not have the privilege of listening to Jesus on a daily basis and witnessing the mighty deeds performed by him. She probably heard of Jesus from others. Yet, when she finally met him, she exhibited a faith that couldn't compare to her knowledge of Jesus. Her great faith enabled her to hear the “rude” statements directed at her, not as an impediment, but as a stepping stone to greatness and as an occasion for her to show her trusting faith. As a pagan, she had nothing to lose. There was nothing that Jesus could say that she hadn’t heard before. She was also aware that what Jesus had said did not take away the fact that he could give her what she wanted. Her patience paid off, and Jesus healed her daughter.