Matt 15:
BDAG:
Did Jesus call her a dog?
She did not react to "dogs" negatively and thereby failed the test. She agreed with the terminology.
That's a deliberate move. Jesus was in a gentile country.21 Jesus went away from there and withdrew to the district of Tyre and Sidon.
Jesus was testing her.22 And behold, a Canaanite woman from that region came out and was crying, “Have mercy on me, O Lord, Son of David; my daughter is severely oppressed by a demon.” 23 But he did not answer her a word.
She humbled herself before Jesus. She passed the first obstacle. Now comes the second:And his disciples came and begged him, saying, “Send her away, for she is crying out after us.” 24He answered, “I was sent only to the lost sheep of the house of Israel.” 25 But she came and knelt before him, saying, “Lord, help me.”
Strong's Greek: 2952. κυνάριον (kunarion) — 4 Occurrences26 And he answered, “It is not right to take the children’s bread and throw it to the dogs.”
BDAG:
Jews were the children. Gentiles were dogs. However, Jesus used the diminutive form of the word, which means house-dogs and not street-dogs. Jesus continued to test her.little dog, dog Mt 15:26f; Mk 7:27f house-dogs that eat the scraps
Did Jesus call her a dog?
She did not react to "dogs" negatively and thereby failed the test. She agreed with the terminology.
She passed the test. She was humble and had faith.27 She said, “Yes, Lord, yet even the dogs eat the crumbs that fall from their masters’ table.”
Jesus praised her, and she had a happy outcome.28 Then Jesus answered her, “O woman, great is your faith! Be it done for you as you desire.” And her daughter was healed instantly.