Instead of following the historical figures that you know best, such as King, it follows the students who were the ground troops in the civil rights movement. What Halberstam makes abundantly clear is how dangerous what they were doing was. Simply, they could have been killed. Some of them very nearly were. And there were people killed, but they obviously weren't around for Halberstam to interview. The corollary to that is he drives home how naked some of the violence against the protestors was.
Something I took away is how sanitized the teaching of the civil rights movement has become. By doing that, we diminish what those young people actually did, and we conveniently forget how cruel humans can be.
Personally, I think history is best taught when it has a narrative. Hence, textbooks are not good at teaching history. Books with a focused topic - which hopefully implies a focused narrative - are much more compelling. I recognize that's probably not helpful to a high school teacher. I started reading history books, on my own, in college.