Passions are just as common in the lower classes as in the higher, and can be set off by the tiniest and least consequential of things. Billy spilling his soup set off such a passion in John Claggart.
The thing is that Claggart's pride prevents him from even conceiving of the fact that his malice toward Billy could be unreciprocated.
Thus, unlikely at is to an outside observer, Claggart perceived Billy spilling his soup as a disguised sign of some antipathy (dislike) toward him.
He has Squeak, a cunning little corporal, come and report to him on Billy's doings. Squeak, noticing that his master-at-arms doesn't like Billy and wanting to please him, elaborates on the most innocent jokes of Billy's to make them seem like digs at Claggart.
Claggart doesn't doubt this for a second because he knows how disliked masters-at-arms tend to be.
In general, Claggart is both careful and cunning as he does everything he can to raise the phantasm of a reciprocal dislike between him and Billy.
In the words of the ever-keen narrator, "An uncommon prudence is habitual with the subtler depravity, for it has everything to hide" (13.4). Claggart, for his part, is determined that the roots of his ill-founded antipathy not be found out.