Jesus wasn't sent to the gentiles...he was sent exclusively to the Jews because of God's promise to make them into
"a royal priesthood and a holy nation". In honor of his promise to Abraham, he had to give the Jews first opportunity and so all of the first Christians were Jewish. After that God invited the gentiles into his family of worshippers. It was actually Peter who baptized the first gentile convert (Cornelius) along with his entire family. This was the first time that a gentile could come to God without first converting to Judaism.
Jesus spent most of his earthly life with Jewish people. But when he was approached by a Phoenician woman, (a Gentile) who begged him to cure her daughter, Jesus said:
“I was not sent forth to any but to the lost sheep of the house of Israel.” Yet, the woman pleaded:
“Lord, help me!” At that, he added:
“It is not good to take the children's bread, and to cast to the little dogs.”(YLT)
To the Jews, dogs were unclean animals so they were not kept as pets. So by alluding to Gentiles as “little dogs,” was Jesus showing prejudice? No, for he had just mentioned his special commission from God to care for ‘the lost sheep of Israel.’ Moreover, by likening non-Jews to
“little dogs,” not wild dogs, Jesus softened the comparison. Of course, what he said tested the woman. Humbly, she was determined to overcome this objection, and tactfully replied:
"`Yes, sir, for even the little dogs do eat of the crumbs that are falling from their lords' table” (YLT) Impressed with the woman’s faith, Jesus healed her daughter immediately.
In this instance Jesus was not addressing a Jewish person, but referring to the keeping of dogs in gentile society as pets for children. The "little dogs" (puppies) would often be fed at the table by their young masters.
A child with a puppy, Greek or Roman statuette (first century B.C.E. to the second century C.E.)