The novel critiques the provincialism of Daisy Miller's home in Schenectady, New York, and her lack of education. The Millers, too, are critiqued both by the Europeans and their rigid American expatriate community for being too friendly with their servants and lax in controlling Daisy's movements and behaviors. The family stays in Geneva and Rome but doesn't behave as their community expects—especially Daisy.
We see this filtered through the consciousness of Winterbourne. Though an American himself, he was schooled through college in Geneva and has lost touch with his native culture. Daisy, for example, seems an oddity to him in her complete Americanism, and he wonders about her:
Never, indeed, since he had grown old enough to appreciate things, had he encountered a young American girl of so pronounced a type as this. Certainly she was very charming, but how deucedly sociable!
Winterbourne mirrors the European attitude that a young woman should not be "sociable." He wonders if she is a "flirt," and while he struggles between that and the idea that she is an innocent, he is critical of how she behaves.
When he speaks to his wealthy aunt, Mrs. Costello, in Rome about Daisy and the Miller family, his aunt responds sharply:
They are very common...They are the sort of Americans that one does one’s duty by not—not accepting.
She is scathing towards the Millers for being so equalitarian that they do not respect the class distinctions so important to Europeans. Daisy scandalizes European society by doing what is considered normal in America: going out with men alone. She especially scandalizes her social set by going out with an Italian man of the wrong class.
In sum, Daisy's Americanism—her open, innocent sociality, her lack of a polished education, and her assertion of her freedom to do as she pleases with whomever she pleases—horrifies European society.