My battery ran out before I could delete. I had another sentence there at first about "unless you call respecting rights an obligation," but I took it out because I didn't want to make a mess. To me an obligation in this context means the thing which is created by a positive right. (IME when someone uses "obligation" for negative rights, it's often for a bad-faith argument relying on the vagueness of "rights" to score a rhetorical point.) The analogous but different thing that some would say arises from a negative right, to me, is properly described another way.

My right to life[0] can still exist without you being obligated not to murder me. It means that I am always justified in self-defense, so if you try to kill me, I'm allowed to kill you back. Except not always. But basically always. Except for the exceptions we can frame a million different ways. In practice, neither of our rights to life are absolute...and so on, down the rabbit hole.

[0] But wait: My natural right? My legal right? In terms of enforcement? Or in some vague sense that I "have" a right and those are words I get to say, and, uh, if you don't like it then I'll say them again? In practice, no one cares. People just say "rights" to mean "I'm right."

Talking about rights is fraught and frustrating and mostly pointless, and my comment wasn't worth writing, but there's nothing I can do about it now.