This exact question has been asked many times here on this MB.
A SUB-PANEL, or REMOTE DISTRIBUTION PANEL, is merely an extension of the main service panel (SERVICE ENTRY). Since the neutrals are bonded to the grounding wires in the MAIN SERVICE PANEL, the grounding wires (bare) and the neutral wires (white) should never be connected in any manner beyond the main panel. However, the grounding wires should be bonded to the sub-panel.
And “objectionable current” may flow on metal parts (grounding wire or metal conduit) when the grounded neutral conductor (white wire) is bonded to the metal case of a panel-board that is not part of service equipment (such as a sub-panel). Occasionally, the wires may come in contact with each other in their jacket causing a short circuit in the grounding/grounded system.
If a neutral wire became disconnected (and, it does happen), the return path for electric current could be along a ground wire. While that itself may not always be a hazard, if that ground wire also became disconnected somewhere, parts of the ground system could be energized. That is NEVER supposed to happen.
The neutral wire is essentially a “low-risk” return path for the electric current in that branch of the system. All of the neutral wires have the same electrical potential…zero. At least, no potential compared to ground. There is, of course, 120 volts of potential difference between a neutral wire and any hot wire in the average residential system.
If one were to touch the metal part of a live neutral wire one should not receive a shock. (Don’t try it!) By tying the neutral to ground at one point (in the main panel), half of the conductors (in a typical 120 volt circuit) have no dangerous electrical potential. Of course, as always, the hot wires are still dangerous.