Jesus gives the woman what she wants because she has the faith to pursue Him as she asks for her miracle. She doesn't back down when He walks away from her, and she doesn't back down when He initially refuses her request. It's frustrating when God doesn't answer our prayers immediately, yet forcing us to persist in prayer can build up our faith. Sometimes we have to earnestly desire the answer and pursue Him to receive what we want. Whether our request is for greater holiness, a healing like this woman sought, or something else, it takes greater faith to pursue a delayed answer than to receive an immediate reply. And perhaps that is why God does delay: not because we're "dogs", nor because He's not willing to give us what we're asking for, but so we will grow in faith in believing that He can produce the miracle we seek even though we don't immediately see the evidence of Him doing so.