. Based on her conversation with Hornbeck, why doesn’t Rachel see Cates as a hero?

Rachel has some understanding of what a teacher does and believes, as she well might in this period of history, that teachers are bound to teach what they are directed to teach. Her vision of Cates is that he is not heroic because he does not do what he is "supposed" to do which is her real explanation of why she would not do what he does.