My answer to your question would be that yes, I feel a sense of loyalty to the school system which I attended. As part of my answer, however, I would talk about the great education I received from warm, perceptive and knowledgeable teachers. By emphasizing the education which served you so well and the people who lovingly provided that education, you focus on what you really want, which is to be a part of that same system and be one of those caring teachers. You want to provide what was given to you. I agree that being familiar with the strengths helps you build from the best part of the school, and you would be in a position to come in and help sooner than someone from outside the area who would have to learn all the things you already know.
My answer would be as follows.
First, I would say that there is a sense of loyalty, because the school is in the town in which I grew up. Therefore, there is a sense of love for the school and the people in the town.
Second, I would say that I am familiar with the strengths and weakness of the school system. Therefore, I would be a good candidate on how to work on the weakness and enhance the strengths of the school.
Third, I would say that I know the type of students that are in the school and how to reach them. The reason for this is once again rooted in the fact that I know the town well.