I know this is old, and the OP is probably long gone, but for others finding this thread...
here's my crack at it:
If you have a closed circuit with current running through it, then you have a load being powered. A resistor. Let's say a light-bulb. If you didn't have a resistor (like the light-bulb) you would have a short circuit and the breaker would trip.
Voltage drops ACROSS a resistor, and it will drop its entire voltage by the time it returns to source (Kirchhoffs law). So with one resistor, all voltage is dropped across that resistor. Meaning if you were powering one light-bulb, you would lose all 120 volts (U.S. system estimate) across the light. That means the white wire coming out of the bulb is theoretically at ground potential.
This 0 voltage potential does not mean there is no current. Current is conserved throughout the circuit, and so is identical to the hot side.
If you touch the hot... you're touching 120volts of potential and you are now a resistor in the circuit parallel with the light-bulb. BAD news.
If you touch the neutral, you are a resistor in parallel ONLY with the neutral wire itself, which has extremely low resistance compared to your body. So technically some current will flow on you, but if you do the math based on resistors in parallel and the low resistance of the wire, it is nearing zero.
Importantly: what happens if the neutral wire you are holding (which was providing the low resistance path back to source) looses a connection and becomes incomplete? (one example might be old wiring that has been bent a bunch of times and is just ready to break... you touch it and it breaks). Now you have become a resistor in SERIES with the light-bulb and the primary path for current to take back to source. Since you are in series, now the voltage drops takes place over both resistors in the circuit (you and the light-bulb) with the largest drop occurring at the higher resistance (you).
Another way to think of the last scenario is to consider that the neutral is only the neutral (or better yet, is only at ground potential) when it is intact all the way back to source. As soon as it is open, it is effectively the hot if there is some load connected upstream. Additionally this all assumes correct wiring, which is best not to assume.