Matt 15:
That's a deliberate move. Jesus was in a gentile country.
Jesus was testing her.
She humbled herself before Jesus. She passed the first obstacle. Now comes the second:
Strong's Greek: 2952. κυνάριον (kunarion) — 4 Occurrences
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.
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.
Jesus praised her, and she had a happy outcome.
It does seem like a strong term; however, I believe that with a little background and interpretation may be necessary.
First, John the Baptizer’s responsibility was to attempt to turn many of the Israelites back to pure worship toward God. (Luke 1:16; John 1:31) Then Jesus and his apostles followed up in this work, toward “the lost sheep of the house of Israel,” by opening blind eyes to the false traditions of men. (Matthew 15:24; 10:6) Yet, only a remnant accepted Jesus as Messiah and was saved.-Roman 9:27; 11:7.
Secondly, to the Jewish nation, Gentiles were likened to dogs of which were considered unclean animals. However, Jesus softened the comparison. His using the term “little dogs” may have been in reference to dogs kept in a home, and not to wild dogs of the street- Nevertheless, what Jesus said was likely to test the woman‘s faith. Rather than taking offense, the woman humbly and correctly interprets Jesus’ reference to Jewish prejudices and continues her plea.
