Debate teaches communication. It is important for students to learn how to shape their ideas and form conclusions. It also helps for them to view a problem or question from different perspectives. Debate is a necessary tool for the growing mind to articulate their thoughts and gather good research to prove or disprove someone's theory or idea. It also helps them to develop confidence and learn how to handle criticism.
Debate should be taught in school because it is important for students to learn the skills it takes in order to effectively debate a topic. Even if they do not agree with their position, it takes skill to talk about the topic and defend the point of view. This should remain in school.
Unfortunately far too many people grow up so sheltered that they may only know one side of an argument their entire lives. Teaching debate in school would force kids to think outside the box and also learn that there are two sides to every argument. It's good to challenge kids to think outside of their personal comfort zone.
I believe debate should be taught in school. I believe it is generally covered when talking about speeches, but I honestly think we need to spend more time on it. I know a lot of adults who are not capable of using facts to support their beliefs yet still want to argue about them. I believe society would be better if people understood how to debate in an effective manner.
When I went to school in the early 90's, debate was taught in school. We had an actual class called, "debate class." It was a requirement by the school board, that it had to be taken. It could be different in different places. It could be because of all the budget cuts of why I always thought everyone had to take debate.