In my view, evolution, human instinct, and human nature have nothing to do with whether or not rights exist or whether or not ethics exist. “Is” cannot determine “ought”.
The key thing is this: what are ethics? why do we discuss them, teach them, and talk about them? (I’m viewing “rights” as a subset of ethics here)
It’s quite obvious that the function of ethics is to provide a means of interacting with one another for our mutual well-being. As such, the judgment over whether something is ethical, or whether something is more ethical than something else, should be based on how it performs in furthering that function.
True Ethics, then, would be that set of human behaviors which, if implemented, would provide the greatest survival and prosperity for the whole.
Because our actions and behaviors have objective effects, then it is objectively true that some actions are more ethical than others. But, since we don’t have a time machine and can’t always know the intricate future consequences of various ethical ideals, then we must make arguments, build our case, look at the evidence, and make estimates about which things better achieve ethical ends. And we must build consensus in that. Nevertheless, there IS a RIGHT answer, that is objectively true. In other words, there IS a selection of behaviors which will fulfill the function of ethics better on the whole (and in the long run) than the others.
As for, say, the right to free speech for example: it will either benefit us on the whole to live in such a world more than not holding and protecting that right or it will benefit us less by doing so. This is an objective fact that we could hypothetically know, were we able to run history twice, changing only that variable.
This is why arguments for various rights (or any ethics) usually involve reasoning on why it is beneficial to protect such rights and then use statistics, psychology, empathy, and other information to try and show why we would be worse off if we didn’t (or vice versa).
I happen to be of the view that there are some things that, if we protect individual’s ability to do through law, we will be objectively better off. This means, by the reckoning I have outlined, that to have these things (i.e. “rights”) IS objectively: ethical. In other words, if my assessment on their effects is correct, rights DO exist and they exist independent of our opinion because they would in fact benefit us even if we thought otherwise and went without them.