Shocking. What can I say? Jesus is a product of His time and culture.
But the woman is desperate to get help for her daughter. She'll try anything and bear any insult--it's worth a try--it may be her last resort. She stays with Him and shows that she's not insulted, she just wants His help. He is merciful and grants her prayer. Deo Gratias.
I found it interesting that she didn't allow a name used as an insult, to insult her. She was focused on obtaining help. The insult wasn't important. And they're not, are they? "Sticks and stones can break my bones but words can never hurt me." Actually, that's true. Although your first inclination is to say, yes words hurt. And I have had my share, and I do know how hurtful they are. But are they? If we let them, they are.
The woman in this Gospel handled being called a "dog" wonderfully. It reminded me of the Order of Preachers, commonly known as Dominicans. Did you know that in their beginning they were known as the hounds of God? At first, it was an insult because they went after the truth like a hound after prey. I can imagine that some friars were as relentless as a blood hound when they were after someone in the Inquisition.
However, the Dominicans turned the insult into a positive identification with the Order. Domini canes is Latin for "hounds of the Lord". They are hounds after Truth. Also, a dog with a torch in his mouth, is one of the symbols of the Order. Dominic's mother had a dream before he was born that she gave birth to a dog with a torch in his mouth. It was predicted that the child who was to be born would set the world on fire with his preaching.
Turning a negative into a positive is the idea. Keep that in mind, next time someone says something hurtful.