In its modern usage, the word "rights" connotes an authoritative relationship between two parties (regardless of the term's original meaning), where one "grants" or at least "recognizes" the rights of the other. This connotation has been the root of my incorrect thinking.
If you take rights to be nothing more than a property of a person (not to be confused with the person's property and property rights), or rather, an "attribute" of a rational, sentient intelligence, then the rest seems to fall into place nicely. Man, being rational, is capable of sustaining his life ("life"), is capable of making choices of how to act and think ("liberty"), and is capable of ownership ("property"). All people have these abilities.
From a computational/object-oriented paradigm:
A man (an object) whom we'll call "Sam" has identity, state, and behavior. His identity is himself, individual, one. His state is rational, sentient, self-aware. His behaviors include taking actions to sustain his life, making rational choices, and acquiring property, in addition to taking actions to defend his rights if they are ever threatened. The invariant of the system is that all men have these rights, which means that infringing on another's rights is nearly impossible to do without invoking that person to exercise and defend their rights. If a second man, "James," were to threaten the Sam's life, Sam is capable of defending himself, either physically or by some other means (firearms, hired thugs). If James were to threaten Sam's property, Sam again is capable of defending his property.
Coercion is the act of infringing upon another's rights to the point where they can no longer defend them, i.e. if James were to subdue and restrain Sam so that he could no longer defend himself, or if James were to shoot Sam in the back. This sucks for Sam and seems good for James in the short run, but in a dynamic system, it's likely that Susan, Joe, and Buck will hear about James' unreasonable and murderous tendencies, and will want to take precautionary measures to isolate the unreasonable (and therefore "inhuman," at least temporarily) James from their community until it appears he will no longer practice coercion.
I know this is very foggy and not at all rigorous - I'm by no means a logician. However, I think the implication of conceptualizing rights this way is important: it is very difficult for somebody to violate your rights without you surrendering them first.