How is Squealer seen as the most important reason for pigs staying in power?
In George Orwell's Animal Farm, we do not meet Squealer until the second chapter of the novel. Whereas Napoleon accomplishes things through intimidation and force, and Snowball is able to capture the imagination of the other animals with his inventiveness, Squealer is regarded as the pig who has the greatest powers of persuasion. In Chapter 2, Orwell tells us that Squealer "could turn black into white."
Squealer's powers of persuasion help convince the other animals that the pigs should be their leaders. In Chapter 4, when some of the other animals murmured about the apples being reserved for the pigs alone, it is Squealer who convinces the other animals that the consumption of such food works especially well to increase the pigs' brainpower. Squealer argues that foods like apples
contain substances absolutely necessary to the well-being of a pig. We pigs are brainworkers. The whole management and organisation of this farm depend on us.
Squealer goes on to argue that if the pigs do not eat such foods and their brainpower is weakened, this will result in the humans coming back and retaking the farm.
Thus, throughout the novel, it is Squealer who puts into words the wishes and commands of the other leading pigs, especially Napoleon. Without Squealer, I would imagine that the rule of the pigs would have been much more bloody than it was, because Napoloen was no orator and relied primarly on force to maintain his leadership of the animals.