| Quote #1
Mayor Peter Stockmann: "I am entitled to request most emphatically that all arrangements shall be […] dealt with by the legally constituted authorities. I can allow no going behind our backs by any roundabout means." (1.103)
The Mayor gets pretty cranky when Dr. Stockmann won't immediately tell him why he's withholding a positive report on the sanitary conditions at the Baths. He's afraid that his brother is doing something outside of the proper political channels. This sort of thing is a direct challenge to system of government that the Mayor represents.
| Quote #2
Billing: "A community is like a ship; everyone ought to be prepared to take the helm.
Here Billing is making a case that everyone should take part in governing society. This is pretty much the basic principle of democracy. Captain Horster, however, points out that's not the way a ship is run. As the captain, he's basically a dictator and everything runs just fine. An Enemy of the People was considered somewhat subversive in it's time because it attacks the basic principle of democracy by saying that majority rule isn't necessarily a good thing. Dr. Stockmann ends up coming to the conclusion that the majority itself is a kind of dictator. In a land where the majority is in control, it is very hard for people in the minority to get a fare shake.
| Quote #3
Hovstad: "what is the most crying need in the humbler ranks of life […] is that they should be allowed some part in the direction of public affairs, Doctor." (2.104)
Hovstad is of the opinion that the way to fix the government is to give the poorer classes more of a voice. It's interesting that though he constantly champions democracy, his calls for the workers of the world to unite against the wealthy sound a whole lot like early communist propaganda.