At one point in Chapter 11, when detailing the antagonism between John Claggart and Billy Budd, the narrator observes that there is no worse place for two men that dislike each other than on board a ship. If you let the observation balloon out into a generality, then we note how confining, how claustrophobic being on a ship can be. There's no way to get a breath of fresh air, you can't get away from your problems, and the result is that little qualms that pass easily on land can spark veritable powder kegs of conflict.
Now, the H.M.S. Bellipotent is a military ship, which means that it is supposed to run like clockwork. The narrator goes to great lengths to emphasize that things are even more tense than usual because our story takes place in the year 1797, during the Napoleonic Wars. The English fleet is trying to protect its country from invasion by the French and at the same time it's worried about upheavals in its own crew. Just a few years before our story a massive mutiny broke out, the Nore Mutiny, and no English captain can go a day without worrying that the same thing could happen on board his own ship. These historic circumstances worm their way into our characters' minds and take on the force of psychological motivation.
A last key detail is that Claggart waits until the Bellipotent is separated from the rest of the English fleet to accuse Billy Budd. Vere, knowing the threat of mutiny, feels obligated to act quickly, to make decisions alone because he doesn't think that he has time to tell the English Admiral. The Bellipotent, alone at sea and doing its best to navigate its course, is itself a perfect image for Captain Vere. Men seem very small in such circumstances, and when there is nothing but water under their feet, perhaps all they can do is look to the laws they know for some sense of stability.For more on the H.M.S. Bellipotent, check out "Symbols, Imagery, Allegory."