Final answer:
Rousseau's ideas were controversial and revolutionary because they challenged traditional doctrines, advocated for direct democracy, and questioned the legitimacy of existing political systems.
Step-by-step explanation:
Rousseau's ideas were controversial and revolutionary for his time because they challenged traditional doctrines and questioned the existing political systems. He advocated for direct democracy instead of representative governments and believed that people should take control of the government to establish a system that serves the 'general will' of the people. Rousseau's views on political liberties and his belief that the social contract was not a voluntary pact entered into by the people made his ideas radical and controversial.