Part (a)

Deedat being dishonest again by selecting a verse and only give half of the story. Yes Jesus only went to the Jews at the beginning of his ministry. That is how the Holy Spirit led Him according to His own wisdom. First the Jews and then the Samaritans (who had a strange, near Jewish religion) and then finally the gentiles (which as a gentile I thank God for). There are many Bible verses that point to the gospel going out to the gentiles in both the old and new Testaments but I will take what Jesus said just before He ascended to heaven after his resurrection; “Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, and teaching them to obey everything I have commanded you. And surely I am with you always, to the very end of the age.”

Matthew 28:19-20

 

Part (b)

I answered the question of going to the gentiles in part (a) but on the question of calling this woman a dog; First thing to comment on is in ancient Greek, there are two words for dog. One is the word kuon (κύων) and the other is a diminutive form, kunarion (κυνάριον) which is used in the New Testament to refer to a small dog or puppy. It is the latter word that Jesus uses. In the ancient Near East, dogs were generally not held in high regard and were often seen as unclean animals. However, the use of "kunarion" as a diminutive form suggests a more affectionate or less derogatory connotation, akin to a household pet. This reflects a nuanced view of dogs in certain domestic settings, contrasting with the broader cultural disdain.

That said, there is more to this narrative. Jesus is drawing out the faith of the woman which is why it leads to him saying “Woman, you have great faith! Your request is granted.” Jesus was always trying to draw out the best from people which is exactly what he did here and it led to God being glorified in front of the other people there as well.