7 Since these things are so, my brethren, let us mortify our members which are on the earth, and be nourished with living bread, by faith and love to God, knowing that without faith it is impossible to be partakers of such bread as this. For our Saviour, when He called all men to him, and said, 'If any man thirst, let him [come] to Me and drink,' immediately spoke of the faith without which a man cannot receive such food; 'He that believes in Me, as the Scripture says, out of his belly shall flow rivers of living water. ' To this end He continually nourished His believing disciples with His words, and gave them life by the nearness of His divinity, but to the Canaanitish woman, because she was not yet a believer, He deigned not even a reply, although she stood greatly in need of food from Him.
He did this not from scorn, far from it (for the Lord is loving to men and good, and on that account He went into the coasts of Tyre and Sidon); but because of her unbelief, and because she was of those who had not the word. And He did it righteously, my brethren; for there would have been nothing gained by her offering her supplication before believing, but by her faith she would support her petition; 'For He that comes to God, must first believe that He is, and that He is a rewarder of them that seek Him;' and that 'without faith it is impossible for a man to please Him.'
This Paul teaches. Now that she was hitherto an unbeliever, one of the profane, He shows, saying, 'It is not meet to take the children's bread, and to cast it to dogs.' She then, being convinced by the power of the word, and having changed her ways, also gained faith; for the Lord no longer spoke to her as a dog, but conversed with her as a human being, saying, 'O woman, great is your faith! ' As therefore she believed, He immediately granted to her the fruit of faith, and said, 'Be it to you as you desire. And her daughter was healed in the self-same hour.'
Source: Letters (New Advent)