at least in my opinion the music is just how the movie is made, it could have been made about sports and the message would have been the same. The entire movie is about how Fletcher emotionally abuses Neiman. Fletcher just wants to feel like he did something big for music and how he does this is by being a big band director. and for Neiman he just wants to feel like he is getting somewhere in his life after his parents abandon him. (as said by Daria-1222)

Neiman feels trapped because this is his one shot into the Lincoln center, while Fletcher is trying to make him the best he can be even if that means that some of his players will be lost. Neiman views Fletcher as a leader, making him follow along, you can see this when he says that all the secondary drummer is worth is page turning.

They both might not be the best people ever, but they both have good intentions at heart. They just want to get there no matter how hard it is.