Some people have a very warped understanding of what constitutes 'duty of care'.
Legal obligation for a person to exercise reasonable care towards another, to avoid some form of harm which is reasonably foreseeable.
The harm in this case doesn't extend to financial issues. If an airline refused travel and turfed people out of a terminal into a riot then they may have breached duty of care. Cancelling a flight in line with the previously advised terms and conditions would not in and of itself constitute a breach of duty of care.
I've got no qualms with saying that I think that airlines have a moral obligation to look after their customers- or at least ensure that their T&Cs are well advertised before people travel- but that shouldn't be confused with a legal requirement.