He did not say that government shouldn't exist, just that it should fear the people, not vice versa. That quote was actually an adaptation of a statement attributed (falsely) to Thomas Jefferson: "where the people fear the government, there is tyranny. Where the government fears the people, there is liberty."
Here is a more accurate version of Mr. Jefferson's sentiments:
The purpose of government is to enable the people of a nation to live in safety and happiness. Government exists for the interests of the governed, not for the governors. As Benjamin Franklin wrote, "In free governments the rulers are the servants and the people their superiors and sovereigns." The ultimate powers in a society, therefore, rest in the people themselves, and they should exercise those powers, either directly or through representatives, in every way they are competent and that is practicable.