In Animal Farm as well as in Soviet Russia, Communism only looks good on paper. The reason that it can't be attained in either case is because when a small elite group has all the power of governing a large group,and controls every facet of life, the small elite group will abuse the power they have and be subject to corruption.
In essence, communism eliminates private ownership and puts control of all economic activity in the hands of the government. The worker is to be provided for and everyone is to be equal.
Technically, in the eyes of the state, or the farm, individuals have no value except for what they can contribute to the state. When Boxer can no longer contribute, he is sent away to die.
However, it is clear that the Pigs and the Dogs do not work the same as the other animals nor do they live the same, and, they control the animal's perception through propaganda, and use of terror to subdue them.
Just like in Communist Russia, the people, the peasants, were told they would be cared for by the benevolent government, and they were betrayed. The same thing happens in Animal Farm, the animals are betrayed by their leader, Napoleon, who begins to abuse them in a far worse manner than the farmer.
So, therefore, when Communism is tried, like in any dictatorship, the powerful enjoy lives of luxury off the backs of the workers/peasants, who are lied to and abused.
The most immediately reason why the worker's paradise can't be realized in Orwell's modern classic is that he is modeling his work on the Soviet Union. Because their attempt to create a collectivist heaven on earth failed, so must the animals' attempt.
Now, if we move to the theoretical level, we start to get into disputed areas. Orwell was a Socialist, so he couldn't have been saying that socialism as such was not possible. Instead, he was arguing the dangers of a centralized state, a powerful leader, and, above all, of allowing a few to gather power and use violence against their own people / animals, including the lies of rewriting history, caused them to collapse to a straightforward tyranny.