How does Napoleon use the sheep’s bleating of “Four legs good, two legs bad” to his advantage?
Napoleon reduces all of the Seven Commandments to the single maxim: "two legs bad, four legs good." This works to his advantage for several reasons: first, it obscures the equalitarianism and specificity of the actual Seven Commandments, which declare that all animals are equal and don't kill each other, and it differentiates between animals and humans in concrete ways: animals don't wear clothes, sleep in beds or drink alcohol. Napoleon thus reduces a manifesto about animal ethics and identity into a mindless slogan. It also becomes a mindless slogan taken on faith, representing the animals' slide into authoritarianism. Tellingly, the birds at first protest that they have only two legs; then, when they can't understand Napoleon's explanation that their wings are like legs, simply accept the truth of the statement without question.
Napoleon drums the statement into the minds of his followers through encouraging its repetition and painting it in big letters on the wall of the barn. It will work in his favor because his followers, especially the sheep, will chant it over and over to drown out dissent. Napoleon, for example, works behind the scenes so that the sheep will start the chant at crucial times to disrupt Snowball's speeches.
Later, the sheep's chanting of "four legs good, two legs bad" will silence protests, such as when Napoleon retires the song "Beasts of England," a seven-stanza song full of images and ideas, and replaces it with the simplistic, short and authoritarian
Animal Farm, Animal Farm,
Never through me shalt thou come to harm!
Later, Napoleon will change the "four legs good, two legs bad" slogan into "four legs good, two legs better," a reversal of the original meaning of the chant.
In Napoleon's manipulation of language, Orwell illustrates one his central theses: the idea that dumbing down the language paves a way for authoritarian and totalitarian regimes to seize and hold power. What we say and how we say it is important, Orwell argues, and animals (and people) need to actively resist efforts to embrace slogans and propaganda.
Basically, what is going on with this is that Napoleon uses the sheep's bleating to drown out anyone else who is trying to speak. That is, he has the sheep drown out anyone who wants to say anything that goes against what Napoleon himself thinks.
You can see this first in Chapter 5. In that chapter, Napoleon has the sheep bleat this in the middle of Snowball's speeches. Later on in the chapter, after Snowball has been chased off the farm, Napoleon has the sheep bleat to drown out anyone who wants to say that Snowball hadn't been bad.