James Chastek, at Just Thomism, discusses one critique of "rights." Here is another:
In America, since at least the Civil War, the fiction of "rights" has been popularly used as a justification for violence, both physical and verbal, against whoever is perceived to be against the "rights" in question. Instead of speaking about justice, morality, virtue, the health of the community or the common good, we only hear of ever expanding rights that only an inhuman or, worse, subhuman creature could possibly oppose.
Once you limit the debate to the categories of those who are in favor of expanding "rights" and those who would deny this expansion, you have created a morality play in which "rights" proponents are angels whose cause is justified no matter the content. The popular arguments over homosexual "marriage" play out in just this way. A practice that makes absolutely no sense from any normal human metric of individual morality or the common good not only becomes acceptable, it becomes the default morally superior position. How can the pendulum swing so hard and fast? This is only possible when the discussion is framed in terms of "rights." Those who stand against such behaviors and actions can, in principle, have no justifiable reason for their opposition. They are demons, and demons do not have to be treated like human beings.