Mark says that Jesus was not able to escape notice after He had come into the house. But why did He go away to these parts of the region at all? When He released them from the observance of food laws, then He finally also opened a door to the Gentiles as He proceeded on the road. This anticipates the similar act of Peter, who first received a command to put an end to this law and then was sent to Cornelius.
But if anyone should say, “Why then does He allow this woman to approach Him when He says to the disciples, ‘Do not go in the way of the Gentiles’?” We first note that He Himself, being who He is, was not, strictly speaking, required to obey the command that He gave to the disciples. We observe, second, that Jesus was not going there to preach. This is the very point that Mark implies when He says both that Jesus hid Himself and that He could not escape notice. The fact that He did not run to them first was consistent with the order of the tasks set before Him. In exactly the same way, driving away people who were coming to Him was unworthy of His love for humanity. For if one should pursue those who are trying to escape, much more should one not try to escape those who are pursuing. …
See her humility as well as her faith! For He had called the Jews “children,” but she was not satisfied with this. She even called them “masters,” so far was she from grieving at the praises of others. She said, “Yes, Lord, yet even the dogs eat the crumbs that fall from their masters’ table.” Behold the woman's wisdom! She did not venture so much as to say a word against anyone else. She was not stung to see others praised, nor was she indignant to be reproached. Behold her constancy. When He answered, “It is not fair to take the children's bread and throw it to the dogs,” she said, “Yes, Lord.” He called them “children,” but she called them “masters.” He used the name of a dog, but she described the action of the dog. Do you see this woman's humility? Then compare her humility with the proud language of the Jews: “We are Abraham's seed and were never in bondage to any man.” “We are born of God.” But not so this woman. Rather, she calls herself a dog and them masters. So for this reason she became a child. For what does Christ then say? “O woman, great is your faith.”
So we might surmise that this is the reason He put her off, in order that He might proclaim aloud this saying and that He might crown the woman: “Be it done for you as you desire.” This means “Your faith, indeed, is able to effect even greater things than these. Nevertheless be it unto you even as you wish.” This voice was at one with the voice that said, “Let the heaven be,” and it was.
“And her daughter was made whole from that very hour.”
Do you see how this woman, too, contributed not a little to the healing of her daughter? For note that Christ did not say, “Let your little daughter be made whole,” but “Great is your faith, be it done for you as you desire.” These words were not uttered at random, nor were they flattering words, but great was the power of her faith, and for our learning.
He left the certain test and demonstration, however, to the issue of events. Her daughter accordingly was immediately healed.
John Chrysostom, The Gospel of Matthew Homily 52.1, 3









