Grace's father says she is arrogant because she doesn't retaliate when people wrong her, rather she rationalizes their behaviour by saying that they're a victim of their environment. He calls this arrogance because it implies that she is morally superior because she can choose to do the right thing, but they cannot. Her father thinks that everyone is equally capable of making moral choices, so when they do, they should face the consequences.
If someone crosses Grace's father, he doesn't excuse them, he shoots them. In the end, Grace performs a volte face, and does the same.
This 'law of the jungle' is only right if you're in the jungle. A better arrangement is to have a Hobbesian leviathan to dispense justice. Then everyone is better off.
The only problem is that films about people dutifully following the correct bureaucratic procedures to ensure the due process of law are boring.
There's more I want to say, but I don't like to go on, so here it is in bullet points:
- The film is too long. If it were published under a CC license I'd shorten it by about an hour.
- I didn't really before, but now I like Nicole Kidman.
- Each resident of Dogville abused Grace. Was Tom the worst because he engineered the whole thing to provide material for his writing?
- The unusual staging of the film worked brilliantly. The only off-note was the miming of the opening and closing of doors.