The statement of human nature that Orwell's Animal Farm is making is that human nature is corrupted by power and greed. Think of the idea of "four legs good, two legs bad" which the animals seem to use as one of their credos. Two legs are bad considering that the animals run off Mr. Jones in favor for Old Major's utopia of animals rule, people do not. This dream state has everyone cheering at first, especially Boxer the cart-horse.
The animals work together and learn to read but then that all changes once Snowball and Napoleon come into conflict. Being the selfish one, Napoleon allows for the puppies he took aside for educational purposes, to run off Snowball. Napoleon felt threatened by Snowball and used the puppies to secure his hold over the other animals. For the good of the other animals, the pigs will make the decisions from now on, announces Napoleon.
After the windmill idea goes forward (originally brought up by Snowball) and then fails when it collapses, Napoleon further secures his power by having the dogs kill any animal involved in the plot to destroy the windmill. It is suggested that Snowball is to blame. Basically Napoleon takes on the view of "you're either with me or against me." This is a common view many dictators and other conquerors have assumed in order to scare the people into following them.
Napoleon then begins to become less like one with four legs and more like one with two legs. He becomes greedy and power hungry. He takes to sleeping in bed like those on two legs and even begins trade with the farmers of the area. These ideas originally went against the animal rules adopted by the farm shortly after Old Major's death.
Further corruption of the pigs by power is how Squealer- Napoleon's cohort, always tells the other animals that they are better off now by having Napoleon as their leader and by being free from Mr. Jones. This is counter to the reality of the animal's situation. The animals are cold, with little food, and all are tired from working harder to satisfy the needs and greed of Napoleon and Squealer.
Sadly this lust for power and greed knows no bounds when after a battle from the destruction of the windmill by a farmer named Mr. Frederick, Boxer is injured and then taken to the glue factory. Though Squealer tells the other animals that the brave Boxer is going to the hospital, the biggest advocate for the farm and Old Major's dream is killed in favor for money for more whisky. Boxer's memory is further tarnished by Squealer insisting that Boxer's last words praised the Rebellion.
“All animals are equal, but some animals are more equal than others,” is the only rule that seems to survive the Rebellion, though altered to meet the needs of Napoleon and Squealer. These words ring true once the other animals crowd around a window to see how the pigs, once on four legs, have now become creatures of two legs. Now it would seem that "two legs good four legs bad," is the better credo for the farm now that the other animals can not tell human from pig anymore, both are sadly the same.