After the animals’ successful rebellion against Farmer Jones, two pigs, Napoleon and Snowball, emerge as the new leaders of the farm. They announce to the other animals that not only have they taught themselves to read and write, but they’ve come up with seven commandments for the animals to live by. Although most of the animals learn to read and write to some degree, it’s only the pigs who are really literate. When some of the animals, including the sheep, have difficulty memorizing the seven commandments, Snowball comes up with the maxim “four legs good, two legs bad” (34). Later, when the animals divide themselves into two factions, those who support Napoleon and those who support Snowball, it’s the sheep who undermine Snowball by repeatedly bleating “four legs good, two legs bad” (48) during his speeches. It’s not long after that Snowball is scapegoated by Napoleon and run off the farm. Reducing the more nuanced commandments into a simplistic maxim points to the dangers of an uneducated citizenry.
Since the tenets of Animalism were too hard for the animals to memorize, Snowball shortened them to "Four legs good, two legs bad." When the chickens inquired further, they were told that for Animal Farm's purposes, their wings could count as legs, thus making them fall into the "good" category. The sheep soon picked up the chant, "Four legs good, two legs bad," and a motto for the farm was born.
This attempt at humor by Orwell also demonstrates that the animals were incapable of abstract thought about their own governance. The animals did not only have to have a mantra, but they had to have it chanted over and over. When Napoleon exiled Snowball, he used the chant in order to drown out any anti-animalism sentiment.
After the seven commandments prove too much for some animals, Snowball comes up with the wonderful line "Four legs good, two legs bad" to sum up Animalism.