Jesus seems harsh in his responses to this woman from the region of Tyre and Sidon. Why would he say such things? To come to that conclusion, though, we have to assume that those scathing comments are aimed at her. I don't think they are. I think they're aimed at the knuckleheads who had the gall to criticize her for, "all her begging." Remember that Jesus wasn't just there to perform miracles, his greater mission was (and is) to make disciples. When he says these things, I think he's winding his disciples up in their furor against her. At the end, when he declares her to have great faith, I imagine that was a bit of a moment of sudden silence from his followers. They had been wrong. They had embarrassed themselves, and Jesus allowed their callous hearts to be put on display. Hopefully, that was formative in making them better disciples.