> the argument isn't about about the REASON rights exist. The argument is about what they are and where they come from.

Tomato, tomahto. An argument about where rights come from is intrinsically an argument about why they exist. The definition of a right you're positing is that it's "something a person has intrinsically". While that may make your arguments that follow from that presupposition logically consistent, the presupposition itself has no merit, and therefore all of the arguments that follow from that definition rely on an unfounded assertion.

> As for the REASON rights exist well... There is no reason, that's like asking the reason why gravity exist or the reason natural laws exist or reason people exist. The answer quite literally is just because they do.

That's simply not true. You can look to the morality that other species have and you realize that what a particular animal deems as "moral" or not (which may stem from whatever their sense of a "right" is) relies entirely on the social structure of that animal, e.g. its sense of fairness, compassion, empathy, theory of mind.

> I was talking about these types of rights from the logical consistency standpoint. Said consistency is what often draws people to this definition of rights most often.

Fair point. However in my view, an argument's conclusions have no merits if the axiom itself is bad. Subscribing to an axiom because it gives you nice logical properties is a basically meaningless way to discover what our rights should be. My argument is that the entire position is flawed and anyone who uses the argument that rights exist because they're intrinsic are starting from a weak position, and thus all the conclusions that follow are weak. Using the logical consistency of the argument as a reason for using the original axiom is totally, fundamentally flawed because corollaries cannot be used to assert the axiom is true (it is a self-referencing logical loop). Using "intrinsic rights" as an argument means there is zero room for debate as everyone will then claim that their rights are true because they said so.