I think this is an interesting story to describe Jesus view of women:
Matthew 15 - 21 Leaving that place, Jesus withdrew to the region of Tyre and Sidon. 22 A Canaanite woman from that vicinity came to him, crying out, “Lord, Son of David, have mercy on me! My daughter is demon-possessed and suffering terribly.”
23 Jesus did not answer a word. So his disciples came to him and urged him, “Send her away, for she keeps crying out after us.”
24 He answered, “I was sent only to the lost sheep of Israel.”
25 The woman came and knelt before him. “Lord, help me!” she said.
26 He replied, “It is not right to take the children’s bread and toss it to the dogs.”
27 “Yes it is, Lord,” she said. “Even the dogs eat the crumbs that fall from their master’s table.”
28 Then Jesus said to her, “Woman, you have great faith! Your request is granted.” And her daughter was healed at that moment.
So here Jesus is depicted as not wanting to help this person because she was not among the "lost sheep of Israel" not because she was a woman. Jesus was put in a particular time and space for a reason and it wasn't to heal everyone who asked of it. According to this scripture his mission apparently included something to do with gathering "lost sheep." This woman was persistent, however, and because of that it intrigued Jesus enough to throw out a riddle. Something that he knew would be meaningful to her.
He calls her a dog to her face and it doesn't phase her at all. Maybe she had been treated like a dog all her life? In any event her reply was incredibly intelligent and it impressed Jesus enough to give her something that didn't necessarily belong to her. He healed her sick daughter, no small feat. It was a gift that was not given to many people. How did the families that did have kids that died feel? Would they feel left out by Jesus? Healing the sick is a slippery sloap at best.
This account shows Jesus' trust in the intelligence of humans not just women. I believe it also shows that Jesus treats woman and men equally. She could have become angry about what had been said or she could become sheepish about it. "Oh, I'm sorry that I thought a dog like me could get the bread of children." She could have said something like that and went on her way, but instead she started debating with him and he could do nothing but grant her request. She was right, if a God falls out of the sky and his crumbs can heal her sick daughter she was OK with that.
-Sab