Often confusion follows when talking about Earth and Neutral.
Instead of calling it a Neutral, think of it as "The other current carrying conductor", or "return current conductor".
An Earth Ground or Bonding wire is only intended to carry " fault current" , and we don't want " fault currents".
When a green ground wire is attached to a chassis, it only purpose is to provide a path to Earth ground if another "Live conductor" should accidently make connection with the chassis. In this case the chassis potential is Zero and if your body provides a path to ground when you touch the chassis, the green ground wire will provide the lowest resistance path to ground and(not though your body)
Assuming residential wiring in the US: The black (120V) wire is the feed, and the white (sometimes called the neutral), is the return current carrying conductor. Back at the Service Entrance box the Whites and ground terminals are bonded (and only here are they connected). Since the return wire (white) carries load current, and has resistance, it can and will develop a voltage drop. Depending on the load current, the drop can be quite high, and thus a shock hazard from the so called neutral wire.
Grounding at the Service Entrance point assures a direct connection to ground, with the lowest voltage drop.