This novellete by Henry James is a story of confrontation. One is that between two cultures - the established Western Europeon society of the late 1700s and the emerging American one, seeking its own identity but nevertheless wanting to "belong." Unfortunately, the affirmation of one excludes the possibility of the other.
Another social issue is the changing role of women. What is the woman's role within the couple and what is her role in society,married or not? How can she affirm her own sexual identity and personal liberty other than within the very limited perimeter of obedient daughter, submissive wife, or dutiful mother?
Daisy discovers that she cannot come and go as she pleases upon European soil. A woman who does so will be tagged as a loose or libertine woman whether she is or not. Daisy is figuratively, then literally, stifled then snuffed out in a social sphere leaving her no "air" or vital space.
A more modern context for such "transcultural transgression" would the dilemma of Muslim women who would integrate into Occidental culture and still cling to the veil (or at least be accompanied in public by a father, brother or another male member but never being allowed to go out alone!).