Denham is looked up to by the other boys as the unofficial leader of the class. Inevitably, this puts him at odds with Braithwaite, and a power struggle ensues between teacher and pupil, which culminates in the famous boxing match episode. As Braithwaite becomes more popular and respected, Denham starts to see him as a threat to his power over the other pupils in class. Moreover, he resents Braithwaite for ripping up his pin-up and feels the need to reassert his authority in class.
A boxing bout seems just the thing for Denham to settle scores. At first, Braithwaite refuses. It's then that Denham drops his boxing gloves at Braithwaite's feet. The gesture is loaded with significance. As well as being a challenge to Braithwaite's authority as a teacher, it also shows Denham's contempt for what he perceives to be Braithwaite's cowardice. Braithwaite understands this, which is why he refers to the looks of disappointment and disgust on the faces of the other boys when it seems like he's chickened out.