What I mean is that these rights are not prevalent in nature. They aren't "natural." They may be just and right, and they may be necessary for the preservation and flourishing of society, but they don't exist in nature, and they cannot be implied to be conferred to us by God, since we don't know God exists. Your argument, which is a good one, is in fact what I am trying to point out. Rights come from the well-reasoned mind.
Interesting that you should inject reason into the situation.
Why would self-preservation and ownership of ourselves and that which we create not be a natural extension, stemming from natural beings of reason?
The converse, according to reason, would be that "rights" per se would be supernatural.