"What are you insinuating? That my people's belief is not on the right path".
Zita was kind of offended by Sango's question. Asking her if she has doubts about the stories passed down from generation to generation, a story containing the foundation of her entire race.
It is the same as asking about the validity of her race's existence, or saying there are doubts about the root of her race.
That came off as offensive in a lot of ways, especially to the elves who take pride in being versed in history more so than any other race living.
Their long lifespan makes it so that they can live and witness three or more generations of other races come and go.
They become witness to thousands of years of civilization, its creation and at the same time, its downfall.
That is what the elves are, the advantage they have over every other race; time and history.