This article takes a close look at a rhetoric strategy, often used in an attempt to preserve an appearance of neutrality in conflicts over rights. This strategy rests on the concept of symmetry, and in particular concerns symmetry between so-called 'positive rights' (described as the right to obtain or have an object, to engage in an activity, or to enjoy a desired state of affairs) and 'negative rights' (the right not to have this object, not to engage in this activity, (...) or to prevent this state of affairs). When a positive and a negative right protect contradictory options, this strategy conveys that they are of equal standing. The article cautions against the risks entailed by this inference. The deceptive nature of symmetry is first examined in the context of procreation rights and subsequently in other contexts, including conflicts concerning freedom of expression, active euthanasia, and abortion. Our conclusion is that the explicit or implicit recourse to the argument from symmetry is a recurrent feature of rights discourse, deserving attention and cautious handling. (shrink)