There's certainly not just one right way, and not all pros do that (e.g., Moose Peterson's D3 settings indicate that he leaves the shutter button enabled to do autofocus), but here's one rationale from Photographing Nature by Ralph A. Clevenger:
“Back-button auto-focus is used by many nature photographers, including me. It lets you activate AF by pressing a button on the rear of the camera with your right thumb. Most importantly, it separates focusing from picture-taking. The shutter release still wakes the camera and fires the shutter, but no longer activates focus.” He also has a “Why do you use that back-button to focus?” section where he explains a bit more, but that's his main reason — he simply prefers a separate button for focus.
One disadvantage of that approach vs. the shutter button (for Nikon DSLRs, at least), is that the button doesn't activate VR, and one might prefer that VR be active while focusing.