Why is the animals' rebellion destined to fail?

The rebellion, or actually the experiment in animal leadership, fails because the animals have the same negative qualities as they humans they overthrew.
It would be more correct to say that some of the animals have these qualities. It's not an accident that Orwell chose the pigs to be the leaders in his fable. Orwell plays on the greedy nature ascribed to pigs in the popular human consciousness. This does not mean that all pigs are like that, and Orwell doesn't show all of them that way. At the beginning of the tale, Old Major, the old wise one, gives a rallying speech in which he tells the animals that all humans do is take, without producing anything, and that the animals have the right to revolt and run their own farm. Old Major is partly correct, but doesn't take into account that once some animals gain a leadership status, they'll begin to act just as Old Major says humans act. A power struggle occurs among the pigs after they take over and Napoleon ousts his rival Snowball. The farm under Napoleon's leadership eventually becomes like a human-led farm, with the final observation that when one looks at the humans and the pigs with, one can't tell them apart.
This, of course, is a parable of the Russian Revolution and the Soviet state in Orwell's time. The Bolsheviks avowedly created a workers' state in which there would be equality for all, but it never happened. When Stalin, the human on whom Napoleon is modeled, took over the Soviet Union degenerated into a dictatorship in which basic rights, rather than being secured for all the people, were denied and millions of people were murdered. In other words, the Communists ended up acting just like the leaders of the capitalist states whom they despised. In Animal Farm the animal leaders similarly become the same as the humans they expelled from the farm.