The concept of inalienable rights is a moral axiom accepted by some (sort of like the existence of a God with certain preferences, in fact, many conceptions of inalienable rights are specifically beliefs about the existence of a God with specific preferences); its not a material fact or a supportable conclusion.
And, of course, people who agree that inalienable rights exist disagree on what those rights are (even those that agree on the names of inalienable rights disagree on the definitions of the rights that those name attach to.)
> It's pretty obvious that they exist, otherwise nobody would really care about murder, rape, theft, fraud, lying, etc.
The fact that some people care about these things establishes that those people have certain moral preferences; it doesn't establish the existence of inalienable rights (in fact, many of the people who do care about these things do so based on justifications other than inalienable rights.)
Of course, the same argument apply to the axiom that the rights don't exist.
However, there is a lot of weight to the argument that there is a common list of universally reprehensible wrongs (murder, rape, etc.). Inferring rights from those wrongs is reasonable and doesn't require much in way of explaining where they come from.
I'm not sure why people are so eager to disprove the existence of rights, to be honest. The wholesale embrace of moral nihilism seems empirically worse. Or at least, more conservatively, empirically untested and therefore risky.
Rights aren't material things, they don't exist in any external sense in any case. A "right" (in the moral, rather than legal, sense), inalienable or otherwise, is a just a statement of someone's moral preference. Clearly, these moral preferences exist in people, and, equally clearly, they differ between people.
> However, there is a lot of weight to the argument that there is a common list of universally reprehensible wrongs (murder, rape, etc.).
No, there's not. Well, I mean, sure, its tautologically true (and unsurprisingly widely accepted) that murder, in the sense of wrongful killing, is wrong.
OTOH, when you try to look for some common universal definition of when killing is wrongful, there's a lot less agreement. (The same is true of the other examples you've named, in the parent on great-grandparent posts.)
So, you've got some vague agreement that there are common names from wrongs, but the actual definitions of the wrongs with those names is different. That doesn't really support all that much of a common idea of wrongs implying a common idea of rights.
> I'm not sure why people are so eager to disprove the existence of rights, to be honest.
I'm not so interested in disproving the existence of rights as in getting people to understand that invoking the idea of "inalienable rights" doesn't really, outside of providing a rhetorical flourish, accomplish anything. Because the existence, and even moreso the definition, of those rights is not universally shared, what the invocation invariably amounts to is a circular argument where the supposedly inalienable right in question is defined in precisely the way needed to support the position the person is arguing for.
Which is perfectly convincing if you already agreed with the conclusion, but entirely unconvincing, if you did not.
"Why should we do (or refrain from doing) X? Because Y is an inalienable right and includes within its scope a mandate to do (or refrain from doing) X." Is just not a meaningful argument.
Unless the discussion is among people who have already agreed to the definition of Y being used.