Why did Jesus call a Canaanite woman a dog?

Matthew 15:21–28

²¹Then Jesus went thence, and departed into the coasts of Tyre and Sidon. ²²And, behold, a woman of Canaan came out of the same coasts, and cried unto him, saying, Have mercy on me, O Lord, thou Son of David; my daughter is grievously vexed with a devil. ²³But he answered her not a word. And his disciples came and besought him, saying, Send her away; for she crieth after us. ²⁴But he answered and said, I am not sent but unto the lost sheep of the house of Israel. ²⁵Then came she and worshipped him, saying, Lord, help me. ²⁶But he answered and said, It is not meet to take the children’s bread, and to cast it to dogs. ²⁷And she said, Truth, Lord: yet the dogs eat of the crumbs which fall from their masters’ table. ²⁸Then Jesus answered and said unto her, O woman, great is thy faith: be it unto thee even as thou wilt. And her daughter was made whole from that very hour.

Mark 7:1–30

¹Then came together unto him the Pharisees, and certain of the scribes, which came from Jerusalem. ²And when they saw some of his disciples eat bread with defiled, that is to say, with unwashen, hands, they found fault. ³For the Pharisees, and all the Jews, except they wash their hands oft, eat not, holding the tradition of the elders. ⁴And when they come from the market, except they wash, they eat not. And many other things there be, which they have received to hold, as the washing of cups, and pots, brasen vessels, and of tables. ⁵Then the Pharisees and scribes asked him, Why walk not thy disciples according to the tradition of the elders, but eat bread with unwashen hands? ⁶He answered and said unto them, Well hath Esaias prophesied of you hypocrites, as it is written, This people honoureth me with their lips, but their heart is far from me. ⁷Howbeit in vain do they worship me, teaching for doctrines the commandments of men. ⁸For laying aside the commandment of God, ye hold the tradition of men, as the washing of pots and cups: and many other such like things ye do. ⁹And he said unto them, Full well ye reject the commandment of God, that ye may keep your own tradition. ¹⁰For Moses said, Honour thy father and thy mother; and, Whoso curseth father or mother, let him die the death: ¹¹But ye say, If a man shall say to his father or mother, It is Corban, that is to say, a gift, by whatsoever thou mightest be profited by me; he shall be free. ¹²And ye suffer him no more to do ought for his father or his mother; ¹³Making the word of God of none effect through your tradition, which ye have delivered: and many such like things do ye. ¹⁴And when he had called all the people unto him, he said unto them, Hearken unto me every one of you, and understand: ¹⁵There is nothing from without a man, that entering into him can defile him: but the things which come out of him, those are they that defile the man. ¹⁶If any man have ears to hear, let him hear. ¹⁷And when he was entered into the house from the people, his disciples asked him concerning the parable. ¹⁸And he saith unto them, Are ye so without understanding also? Do ye not perceive, that whatsoever thing from without entereth into the man, it cannot defile him; ¹⁹Because it entereth not into his heart, but into the belly, and goeth out into the draught, purging all meats? ²⁰And he said, That which cometh out of the man, that defileth the man. ²¹For from within, out of the heart of men, proceed evil thoughts, adulteries, fornications, murders, ²²Thefts, covetousness, wickedness, deceit, lasciviousness, an evil eye, blasphemy, pride, foolishness: ²³All these evil things come from within, and defile the man. ²⁴And from thence he arose, and went into the borders of Tyre and Sidon, and entered into an house, and would have no man know it: but he could not be hid. ²⁵For a certain woman, whose young daughter had an unclean spirit, heard of him, and came and fell at his feet: ²⁶The woman was a Greek, a Syrophenician by nation; and she besought him that he would cast forth the devil out of her daughter. ²⁷But Jesus said unto her, Let the children first be filled: for it is not meet to take the children’s bread, and to cast it unto the dogs. ²⁸And she answered and said unto him, Yes, Lord: yet the dogs under the table eat of the children’s crumbs. ²⁹And he said unto her, For this saying go thy way; the devil is gone out of thy daughter. ³⁰And when she was come to her house, she found the devil gone out, and her daughter laid upon the bed.