Benjamin's basic flaw is his negativity. He is cynical and never believes anything can change for the better. His life philosophy can be summed up by his statement after the Rebellion that:
life would go on as it had always gone on—that is, badly.
Benjamin is similar to the person in real life that my students call a "buzz kill." This is the person who always manages to destroy the mood of a good time. After the Rebellion, as the other animals are celebrating the moment by dancing around joyously, Benjamin is already predicting doom.
Benjamin is similar as well to the person in real life who wastes his very genuine talents because he doesn't see any point to anything. In the story, Benjamin is a highly perceptive and intelligent animal, seemingly as smart as the pigs, but he doesn't use his knowledge or insight to help the other animals until after it is too late. He is the animal who could have stepped up to the plate and helped guide the other animals to stand firm against the pigs, but he has already sourly decided from the start that everything is hopeless.
Benjamin is a foil or opposite to his friend Boxer. If Benjamin is overly pessimistic, Boxer is overly optimistic. Neither attitude, the book illustrates, is particularly helpful when one is faced with an evil regime.