Something is not rational just because someone calls it so. A rational argument is the best possible argument you can make because it incorporates all relevant information in direct proportion to its relevance. If relying on that isn't better, then there is no hope for improvement. Rationality is (as far as I know) the only known way to systematically avoid arbitrary errors.
The problem that everybody thinks they are rational and that they don't know what rational means is not a problem with rationality. It's a problem with irrationality.
At what point do you make those rational arguments flesh? Rights[1] would seem, at their core, to be reified rational arguments. As in: over a long period of time, a rational argument as to how a certain group should be treated/not mistreated (prisoners should not be tortured, say, or women should have the same opportunities as men) is made many times. Eventually its rationality may be accepted, and eventually reification may occur. Relying simply on rational arguments seems a. heavily constrained by bounded knowledge, b. extremely susceptible to interference and c. produce much more fragile legal structures than rights infer.
In respect to the OP, setting down the rights of Orangutans surely is making a rational argument, then allowing that argument to be applied in all similar cases, rather than making the same argument repeatedly?
[1] as fought for cross-culture/worldwide/etc (eg human rights) and positive, not culture-specific & negative (eg rights of one tribal group over all others in a country).
I'm not sure what you're trying to ask. The core problem with rights is that they are weaker than rational decision-making, and thus they are fundamentally flawed. Rights can be (and should be) revoked by 'very good reasons'. And it stands to reason that they should be established by comparatively strong measures.
So if rights are always secondary to rational arguments, what extra value do they bring to the ethical picture? They only mean anything if you are making irrational decisions, 'blindly' protecting them and whatnot.
>[rational arguments] produce much more fragile legal structures than rights infer.
I don't believe this, and I don't think there are any examples to suggest this. Laws are notoriously less flexible than they would need to be to be engines of rational decision-making, and thus there are no 'rational' legal structures. The fact that we have judges, juries, and opportunities for defense against the law are constructs that we invented to inject rational flexibility into a legal systems which would otherwise be blind draconian monoliths.
But this means you step outside of the legal structure and into the ethical structure of the minds involved: a judge/jury can rule that, even if you violated some law, you might be _justified_ in doing so and should not suffer any consequences. This kind of argument is often made in terms of rights, but then, so are the laws that are being ignored. One must always apply a rational argument, because every right is in conflict with some other right -- being that they are vague, underspecified things to begin with.
The problem that everybody thinks they are rational and that they don't know what rational means is not a problem with rationality. It's a problem with irrationality.