Daisy Miller is not only one of the great American literary heroines but she might be the quintessential American heroine.
Allow me to explain.
Henry James has a certain contempt for American society, specifically the way the American upper class DESPERATELY want the approval of European society. To the extent of alienating themselves from their American identity to make themselves more appealing to Europe and European propriety.
But into this steps Daisy Miller, a young woman who gleefully refuses to play by the rules of European decorum or American social climbing. She's here to live fearlessly as long as she can, to the chagrin of the American elite. She kind of forces them to say the quiet part out loud or get out of her way.
And James' critique isn't just cultural and class based but gendered as well. Our narrator Mr Winterbourne adores Daisy with all her quirks and charms, until she directed them at another man. At which point he switches allegiances to the rest of the Americans abroad.
Men want a spirited woman, until she makes her affection for them ambiguous, or even makes it clear her affections are for another man.