The narrator doesn't know a lot about John Claggart – just like he doesn't know a lot about Billy Budd. Early on in the story, the narrator notes that, if he provided some background, he "might avail in a way more or less interesting to account for whatever of enigma may appear to lurk in the case" (11.2). In other words, Claggart wouldn't be such a mystery if the narrator would just give us a few incidents showing why Claggart hates Billy.
But there's a catch. According to our narrator, there is no background. Nobody knows why Claggart hates Billy. As he tells it, that's just the way things are. It is a mystery.
The fact that we don't know the source of Claggart's hatred for Billy has some strange effects on how we perceive the character. As soon as the narrator finishes telling us that nobody knows why the master-at-arms is the way he is, he begins speculating. The more the narrator speculates, the easier it is to forget that none of what he is saying is rooted in fact, that the descriptions are just composed of the narrator's thoughts and opinions. Think of it this way: his idea of Claggart becomes our idea of Claggart.
So what is the narrator's idea of John Claggart? Well, he says that Claggart has "the mania of an evil nature, not engendered by vicious training or corrupting books or licentious living, but born with him and innate, in short 'a depravity according to nature'" (11.9). In other words, the narrator looks at what he knows of Claggart's experience and can find no reason for him to behave in such a cruel way. He concludes that whatever evil there is in Claggart is "innate," that it was put there by "nature." The result is that Claggart is portrayed as the antithesis (the exact opposite) of Billy Budd. Whereas Billy is almost completely good, Claggart is almost entirely evil.
Here's a question that you can sink your teeth into: if Claggart's evil is "innate," then can he really be held responsible for it? Isn't that like trying to hold him responsible for his height or the shape of his chin?
At times, the narrator himself seems to be making this argument. He often presents events as if Claggart has no control over his behavior. He says that Claggart must, "like the scorpion for which the Creator alone is responsible, act out the end allotted to it" (12.4). Later, he says that Claggart's evil, "like a subterranean fire, was eating its way deeper and deeper in him. Something decisive must come of it" (17.10). It's almost as if Claggart is possessed, as if evil is just acting through him and he is not in control of his actions.
Again, let's remember that this is how the narrator describes Claggart. It's not necessarily the way that Claggart is. For a morality story, it's pretty nice to have good and evil be polar opposites, to each be neatly embodied in one character. But the result is that Claggart doesn't come across as a full character, that the narrator is describing the conflict between good and evil, rather than the conflict between two men.
The problem can be seen most clearly when the narrator describes Claggart's eyes after he accuses Billy of treason. The narrator says, "Those lights of human intelligence, losing human expression, were gelidly protruding like the alien eyes of certain uncatalogued creatures of the deep" (19.4). The key phrase here is "losing human expression." After that, the narrator says that Claggart has "alien eyes." He has made Claggart completely inhuman, evil and incomprehensible. It's almost as if Darth Vader died before he got a chance to take off his helmet and reveal himself as a man.
Above, we've made the case that Claggart is presented as inhuman, as pure evil. But the thing about Billy Budd is that it's almost impossible to only argue things one way. One might say that Billy Budd is actually a big book posing as a small book. Within its pages, things become fleshed out and nuanced and ambiguous in a fraction of the space that it takes other authors to achieve such effects.
For all the narrator's talk of Claggart as evil embodied, he seems to give himself away early on in the book. When he is recounting all the rumors about the master-at-arms, he then reigns them in by noting that "sailor as much as landsmen: they are apt to exaggerate or romance it" (8.4). The narrator often tries to present himself as being better than the average sailor, but it's also clear that there is much of the sailor's spirit within him. When he begins describing Claggart, he often gets carried away to the point that one might think he is describing evil itself.
At other points, though, the narrator is more realistic. Trying to explain Claggart's hatred, he appeals to just how common such "gut feelings" are:
For what can partake of the mysterious than an antipathy spontaneous and profound such as is evoked in certain exceptional mortals by the mere aspect of some other mortal, however harmless he may be, if not called forth by this very harmlessness itself. (11.2)
On the one hand, the narrator is arguing that Claggart is an "exceptional mortal," but on the other he is trying to render Claggart's hatred normal and understandable.
According to one of the narrator's hypotheses, the root of Claggart's hatred is actually incredibly petty. He's simply jealous of Billy's "significant personal beauty" (12.2). The narrator notes what an embarrassing sin jealousy is when he asks, "Well, though many an arraigned mortal has in hopes of mitigated penalty pleaded guilty to horrible actions, did ever anybody seriously confess to envy?" (12.3). The way he depicts things in this version is that Claggart is so ashamed of his envy that he tries to hide it from himself. The result is that his envy festers like a sore and turns into something much worse: uncontrollable, incomprehensible hatred. Yet the root remains petty jealousy. It's an entirely human fault, but one that gets blown out of all proportion in the case of Claggart.
Perhaps nowhere is John Claggart more sympathetic than the moment the narrator tells us that as he passes Billy his eyes are "strangely suffused with incipient tears" (17.2). The narrator reads into such an expression, "soft yearning, as if Claggart could even have loved Billy but for fate and ban" (17.2). We here get a glimpse of Claggart as a man in the grips of a hatred that he himself doesn't understand. In a way, it is, once again, the idea that Claggart is possessed, that he's not entirely in control of his actions. The point though is that this is the exact opposite of the dehumanizing image we get of Claggart after he accuses Billy Budd. Though he is about to do something terrible, Claggart comes across as a human being, someone we can understand and to whom we can relate.