Why did Jesus refer to the Gentile woman as a dog?

When Jesus referred to the Gentile woman as a dog, He was not demeaning her but rather using a metaphor to explain His mission's focus on Israel first. This encounter highlighted the uniqueness of His ministry, which was primarily aimed initially at the lost sheep of Israel. However, the woman's humble response showcased great faith. Her recognition of her desperate need for mercy amid His words demonstrated that genuine faith acknowledges its unworthiness before God while still seeking His grace. This exchange is pivotal in illustrating how faith transcends ethnic and cultural boundaries in Christ's redemptive plan.