Snowball is the one who reduces Animalism to the simple maxim "two legs good, four legs bad," and then Napoleon makes use of it to distract proceedings.
Snowball reduces the principles of Animalism down to something that all animals can understand.
After much thought Snowball declared that the Seven Commandments could in effect be reduced to a single maxim, namely: "Four legs good, two legs bad." This, he said, contained the essential principle of Animalism. (Ch. 3)
From there it gets a little more complex. It says that the sheep “developed a great liking for this maxim” on their own. At first, Napoleon is not interested in Snowball’s committees, the sheep, the maxim, or anything else. However, Napoleon soon has the sheep’s support and they are interrupting Snowball’s speeches with “Four legs good, legs bad” (Ch. 5). The sheep are excellent at breaking up meetings.
Snowball believes in Animalism. He wants the animals to have communal ownership of the farm, and take care of themselves. He wants every animal to have ownership, and have a purpose. He believes they can do it without the humans. He does not want power for himself. He is therefore a great threat to Napoleon, who only wants power. This is why Napoleon runs him off, and tells the other animals that he was a criminal.
Even after Snowball is run off, between pigs squealing and Napoleon’s guard dogs growling, all it takes is the sheep to break up a meeting.
Then the sheep broke out into a tremendous bleating of "Four legs good, two legs bad!" which went on for nearly a quarter of an hour and put an end to any chance of discussion. (Ch. 5)
Soon there is nothing resembling a meeting left. The animals are afraid to make their voices heard, or even assemble. The sheep have successfully become Napoleon’s minions. While they might have started out with the purpose of actually supporting Animalism, by the end they are just brainwashed or afraid. Napoleon and the pigs control everything.
The animals began with an ideal. They wanted to control the farm themselves, and everyone would have an equal voice. However, while Snowball might have believed in those principles, Napoleon co-opted them for his own gain. He used the sheep, and the other animals, to get power for himself. Four legs really was no different than two legs for the animals. They just traded one abusive tyrant for another.