Perhaps the most important social factor that helped to end the Han Dynasty was the idea of the "mandate of Heaven." This idea, which came from Confucianism, held that a country would have good fortune so long as the government really had the approval of the gods. If bad things were to happen, this would show that the gods had withdrawn their approval of the government.
As the Han Dynasty became weaker, bad luck also struck China. There were a series of natural disasters like floods and famines that afflicted the agricultural areas of the country. Because of the idea of the mandate of Heaven, these disasters were taken by many as a sign that the gods no longer approved of the Han Dynasty's rulers.
As people came to believe this, they were, of course, more likely to be willing to oppose the Han government. This led to rebellions such as the Yellow Turbans Rebellion in which rebels were led by religious leaders who promised a utopian society would ensue.
Thus, the Confucian idea of the mandate of Heaven came to be a major social problem for the Han as their dynasty collapsed.