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, though determined to overcome this objection, she tactfully replied: “Yes, Lord; but really the little dogs do eat of the crumbs falling from the table of their masters.” Impressed with the woman’s faith, Jesus healed her daughter immediately. (Matthew 15:22-28)
During Jesus’ earthly ministry, he confined his preaching of the good news to the Jews and proselytes, saying: “I was not sent forth to any but to the lost sheep of the house of Israel.” (Matthew 15:24) When sending out the 12 apostles, he commanded them: “Do not go off into the road of the nations, and do not enter into a Samaritan city; but, instead, go continually to the lost sheep of the house of Israel.” (Mt 10:5, 6) On one occasion he preached to a woman of the Samaritans, who were related to the Israelites, but this was not because he had gone into the city to preach. However, the response of the woman and others was so favorable that Jesus stayed with them for two days. (John 4:7-42)
After Jesus’ death and resurrection, he gave his disciples the command: “Go therefore and make disciples of people of all the nations, baptizing them in the name of the Father and of the Son and of the holy spirit, teaching them to observe all the things I have commanded you.” (Matthew 28:19, 20) He also told them that their preaching would reach to “the most distant part of the earth.” (Acts 1:8) But for about three and a half years afterward the holy spirit led the disciples to confine their preaching to Jews and Samaritans. Then Peter was sent by God to bring the good news to the household of the Roman army officer Cornelius. (Acts chaps 10, 11; 15:7) From that time on, the good news was declared to the greatest possible extent over the widest area.