This is a telling result from Google’s Ngram viewer:
It seems that once upon a time people believed that duties were more important than rights (or, which we assume is the same thing, people wrote more about duties than about rights). This time ended somewhere in the late 1800s. Some would call this the era of morality. The era that followed it would then be the era of “ME”, of individualism, of people’s nascent and by now “overwhelming” urge to claim things for themselves, and to claim them from others, from society and from the state. There is indeed a venerable school of thought that sees rights as amoral or even immoral and as the favorite tool of modern individualists and egoists.
Somewhat surprisingly, one origin of this idea is Marx. Nowadays, however, it’s associated more with conservatism and with so-called collectivist and harmonious “Asian” societies (with or without a history of communism). Or maybe it’s just associated with the self-appointed representatives of those societies, namely the often authoritarian leaders there. Not surprisingly, those leaders are the first beneficiaries of harmony and of a widespread sense of duty.
None of this should be understood as a rejection of the notion of duty. Far from it. One person’s rights are another person’s duties. (See also here). In a sense it is indeed regrettable that duties are apparently going out of fashion.