If you’re going to break it down that far, why stop? Your “self” is not your central nervous system, but a portion of it - and not a very large one. It’s your consciousness. Most of what your nervous system does is not conscious.
Your self (and mine) are but a small portion of a single organ in a large network of organs and tissues and cells and bacteria. We developed because it was advantageous for our bodies - which predate our consciousness - to have pilots. We are periphery. We are a single part of an ecosystem. And definitely not the center of it