What did the Duchess do that bothered her husband?

The Duke blames the Duchess for not seeing any difference between being the wife of a "great man" and: being able to see the sunset; receiving a bouquet from someone of status below the Duke's; or riding a white mule. While he thinks it's fine to be courteous ("She thanked men,-good!"), she gave all men the kind of respect that only a man with his family's rank and distinction deserves.