I think the general cause of the "disagreement" between Gene and Quackenbush is that Quackenbush is a generally antagonistic person all around. Gene says that there is something wrong with Quackenbush, and that could be a legitimate mental or physical disorder, but it could also mean that the problem is that Quackenbush is just an all around jerk to everybody. Gene tells his readers that Quackenbush has earned himself a reputation that is generally disliked by all.
Quackenbush was the crew manager, and there was something wrong about him. I didn’t know exactly what it was. In the throng of the winter terms at Devon we were at opposite extremities of the class, and to me there only came the disliked edge of Quackenbush’s reputation. A clue to it was that his first name was never used—I didn’t even know what it was—and he had no nickname, not even an unfriendly one.
The exchange between Quackenbush and Gene supports this notion that Quackenbush is the type of person that is just generally looking for a fight and/or to get under somebody's skin. From the first thing that he says to Gene, it is clear that Quackenbush is trying to push Gene's buttons.
“Late, Forrester,” he said in his already-matured voice. He was a firmly masculine type; perhaps he was disliked only because he had matured before the rest of us.
“Yes, sorry, I got held up.”
“The crew waits for no man.” He didn’t seem to think this was a funny thing to say.
By the end of the day, Quackenbush has not let up on antagonizing Gene, and it's fairly clear that Quackenbush is trying to get Gene to angrily vent or push him toward a fight. To Gene's credit, he stays fairly calm and expresses to readers that he now understands why Quackenbush is hated by everybody.
For Quackenbush had been systematically disliked since he first set foot in Devon, with careless, disinterested insults coming at him from the beginning, voting for and applauding the class leaders through years of attaining nothing he wanted for himself.
Quackenbush finally hurls an insult directly at Gene that involves swearing and calling Gene "maimed." By this point, Gene has had enough, so he punches Quackenbush. Quackenbush's choice of words is unfortunate for him because the word "maimed" reminds him of Finny's injury and Gene's role in that injury. Gene tells us that he punched Quackenbush as a way to defend Finny's honor.
I fought that battle, that first skirmish of a long campaign, for Finny. Until the back of my hand cracked against Quackenbush’s face I had never pictured myself in the role of Finny’s defender, and I didn’t suppose that he would have thanked me for it now.