He wants Betsy but can't be with her and he sees Palantine as the man who she is more interested in. He goes mad and wants to kill Palantine as a result but his plan doesn't work. You could make the argument that his side of the friendship with Iris is not entirely platonic and because of his feelings of guilt about her age, he cannot have her either so he decides to kill the man who she is more interested in: Sport. If Travis succeeds in killing Palantine then he is a villain but because he fails and kills Sport instead he is deemed a hero. The actions and reasoning are exactly the same, he's just an unhinged maniac and society is the one that makes him seem like the well intentioned hero that he appears to be.
