How does a "break" in the neutral wire enable it to reach the full line voltage?
Here is a simplified version of AC power lines:







simulate this circuit &ndash; Schematic created using CircuitLab

The two lines at lower right represent you holding the neutral. Since the neutral is connected to ground elsewhere, as you agree you only feel a small voltage. Note that the load is fairly low resistance, so it can produce a lot of power.

Now let's break the neutral







simulate this circuit

Current will now flow through the upper hot wire, through the load, through you and then the ground in order to get back to the transformer neutral. And since the load has a low resistance, you are the big resistor in the circuit, and you will take most of the voltage.