The Problem With Comparisons
Merely pointing out a contradiction is not enough -- since every contradiction involves at least two terms, there are at least two ways to resolve it (assuming there's no way to rebut the claim that a contradiction exists). In general, people will resolve contradictions by changing 1) fewer beliefs, and 2) weaker beliefs. Thus, the trick for someone trying to get others to change a target belief is to find a contradiction between that belief and a more-strongly-held one. Further complicating things is the fact that the strength of a belief is not just a matter of subjective commitment, but also the belief's percieved social stability.
All of this I think helps to explain why arguments that compare oppressions are so appealing to those who use them but so problematic in practice. Take, for example, the "marginal cases" argument for animal rights. This argument says, roughly: Most people say animals do not have rights, but all humans -- including humans with severe mental disabilities -- have rights. However, animals and severely mentally disabled people are alike in all relevant respects that could be the basis for ascribing rights (they both feel pleasure and pain, neither can talk, etc.). Or, in schematic form, there is a contradiction among:
X -> Z
Y -> ~z
To the animal rights activist making this argument, the solution is obvious: toss out the second premise (animals lack rights). In doing so, the animal rights activist is using the first premise (severely mentally disabled people have rights) as a sort of lever, a fixed point around which other premises have to adjust.
To the disability rights activist, on the other hand, the implications are rather different. While the animal rights activist takes the rights-holding of all disabled people as given and uncontestable, the disability rights activist is keenly aware of the many ways that severely disabled people's rights are denied in practice (even if few people might admit so starkly to believing disabled people have fewer rights**). There are then two problems.
First, the ongoing struggles of disability rights activists are erased by the casual treatment of their cause as already settled. (Melissa and Renee have longer treatments of this phenomenon in the context of comparing gay rights to black civil rights.)
Second, the weakeness of the first premise means that it may be the one to fall when people strive to resolve the contradiction. The disability rights activist may be free enough of false consciousness and internalized self-doubt, and open enough to the possibility of animal rights, to not personally fall into this. But their understanding of the way disabled people's rights are routinely denied presents the choice as a real one, and makes them aware of the danger in how other, less progressive, people may respond. (The fact of this threat may also create a strong motivation to deny that the alleged contradiction exists at all, i.e. to deny premise 3 -- in this case, by finding some other grounds for ascribing rights that would apply to people with severe mental disabilities but not animals.)
My point here is not that certain contradictions should simply be ignored. Rather, it's that it is best resolved by finding a different route to weaken the target belief, one that does not threaten another belief that the argument-maker presumably wishes to retain but which is not so well-suited to be used as a lever.
*Actually, most ethical "debate" consists of trying to raise clashing emotional responses. But I think (pace Bourdieu) the logic of affect is close enough to the logic of propositional statements that most of my post applies to both realms.
**Indeed, this clash between professed position and practice makes this type of argument all the more troublesome, since it's the widespread and sincerely-believed claims about the first group's rights that make them an appealing lever to use in proving the second group's claims.