There is an overall critique of 'rights' as a moral category. A lot of it is captured by Glendon, who is discussed here: http://www.theamericanconservative.com/articles/whats-wrong-with-rights/. It has many dimensions, but some of them are easy to capture as logical contradictions.
First, they are categorical, they are either being violated or they aren't, and life is not that binary. So you can have contradictions like the notion of the right to life in a world where everyone dies, leading to insane expenditure to save an individual life that then depletes resources and causes others to die. So we don't really have the right, we have the wish we had the right, and the obligation to consider those wishes somewhat equally.
Second, they are adversarially posed, so they lead to the construction of enforcement mechanisms that often automatically break them. The right to order and stability, maintained locally by the existence of states, more globally creates wars in which humans are swept into chaos and violated in unspeakable ways. So we don't really have the right, we simply have the opportunity to control how it gets expressed when it happens to exist.
Third, they are individual. We can mandate a right to property, but some property is only useful if it is shared. Property rights to a waterway, for instance mean nothing if someone uses their property right to the part upstream from you to build a dam and divert the water. Then the waterway to which you have the property right does not exist. So neither of you really have that right, you have something more complex and negotiated that cannot really be framed as a right on either party's part.
Fourth they automatically create responsibilities, but do not assign those to anyone. We may consider it a right to have a fair and impartial justice system. But that doesn't mean that our justice system won't make itself corrupt and racist. So again, we don't really have the right, we have the obligation to hold the intention to have the right, so we fix these problems when they arise.