The narrator notes that great passion does not always arise from great circumstances, but can be provoked by trivial things, like Billy's spilled soup. The narrator thinks that Claggart must have interpreted the soup as a deliberate affront to him, because of what Squeak (a corporal serving under Claggart) had told him.
The narrator, after initially saying that Claggart's hatred toward Billy was a total mystery, now continues to speculate about its cause. This can be taken as a metaphor for how all humankind operates, always making up stories to explain what they see happening in the world and between other people. Always trying to explain the unexplainable mysteries of the world.
Claggart had been ordering Squeak to carry out small pranks on Billy and Squeak, guessing that Claggart didn't like Billy for some reason, had been making up rumors that Billy was insulting Claggart behind his back. Thus, the narrator thinks, Claggart thought the spilled soup was a sign of disrespect and made the event into a much more significant issue than it really was.
Claggart's lack of loyalty to his comrade Billy has expanding effects. Squeak senses Claggart's dislike and spreads false rumors to satisfy Claggart's feelings, thus increasing those feelings. And, at the same time, false rumors eat away at the bonds of comradeship that should ideally unite sailors aboard the same ship.
The narrator guesses that Claggart's persecution of Billy was originally intended as a way of making a trial of his innocent character, to see how Billy would react. But as it did not lead to any kind of reaction worth reprimanding, Claggart became frustrated. The spilling of the soup offered Claggart a reason to dislike Billy, and he gladly seized upon it as justification for his animosity toward the innocent young sailor.
In seeking an explanation for Claggart's behavior, the narrator keeps trying out new stories, iterating from one to the next as he tries to find one that makes sense. Now the narrator sees Claggart as essentially frustrated by Billy's innocent nature, as disbelieving such a nature could exist and wanting to put it to a test to prove it. Yet as Claggart's test failed to disprove Billy's innocence, Claggart did not give up but instead became even angrier, as now Billy did not fit into Claggart's view of the world (which held that such innocence didn't exist, possibly because Claggart himself lacks any such innocence). Claggart's hatred of Billy does therefore (as the narrator now sees it) doesn't arise from any specific action like the spilling of the soup; rather, that action is an excuse to justify the dislike Claggart instinctively feels for Billy and Billy's innocence.