At first, the animals are on track to liberate themselves from their human oppressors. However, this initial unity of animals eventually devolves into a segregated class system. One of the initial commandments of Animalism was that "all animals are equal." It becomes pretty clear, certainly after Napoleon takes control, that this is not the case. In fact, the commandment is rewritten to read "all animals are equal, but some are more equal than others." The controlling class (Napoleon and others) literally rewrite the commandments and thus, rewrite history in order to suit their growing greed and in order to sustain their power over the other animals. The so-called lower classes of animals consent because they believe in the albeit shifting propaganda and because they believe in the revolution.
As this is an allegory of the Russian Revolution, you may conclude that people take part in their own oppression because they are persuaded by propaganda and because they are habitually used to some form of authority. The fact that Napoleon was one of their own makes it hard for them to realize that he has become as corrupt as those whom he replaced. Moses is also a tool of pacifying the animals by promising them a reward (afterlife -Sugarcandy Mountain) which is a way of compensating them for their current suffering. Governments and institutions will use such techniques in order to pacify those whom they oppress. The oppressed take part in their own oppression when they allow it to happen. In the case of a revolution, this realization may come later (or too late) since the purpose of a revolution, such as this one, is to liberate the oppressed.