The motto “Four legs good, two legs bad” starts as a chant to help the animals remember the principles of animalism. As the pigs begin to overthrow that system, they take the phrase to drown out opposing opinion. The sheep bleat it out, attempting to literally drown out the opposing opinions being voiced by the hens. As the needs of the pigs change, they eventually change the slogan to “four legs good, two legs better”.
It isn’t just something to drown out the “wrong” opinion anymore; it is meant to make everything obey their rules. Communist societies. What happens to the slogans happens because the ruling power will cling to their power, no matter what the people (or animals, in this case) think.