You’re making useful points but you’re also just choosing convenient definitions that make your point of view “correct”.

The parent comment has a definition of “rights” that admits their existence… and I think what you’ve demonstrated is that you have a different definition of “rights”. In other words, you’ve demonstrated that you haven’t really grasped the underlying meaning that the parent comment is getting at, and you’re instead responding to the words that they used to express it.

If you start with a definition for “rights” you can make arguments about whether they exist. But if you start with a different definition and get to a different conclusion, it doesn’t mean you’ve discovered some logical flaw in the argument, it just means that the two of you have failed to communicate with each other.

I appreciate your analysis, but another way to consider this discussion is that asserting the existence of "rights" is an unsupported conversational maneuver that frames the debate. The grandparent is defining a concept into existence, which is a questionable move IMO, despite being tradition.