Effectively, it's not that the hot wire forces electricity for 1/60th of a second and then the neutral wire does, it's that the hot wire forces electricity for 1/60th of a second and then sucks it back for 1/60th of a second.

In other words, if you stick a multimeter in an electrical outlet, you get 120V between hot and ground and between hot and neutral, but you get 0V between neutral and ground. You can stick your tongue in the neutral side of a socket and leave it there all day long. (Note: I do not suggest this.)

The reason that it has to be plugged in the right way around is for safety. If the 2-prong device you're using fails and shorts, it needs to make sure that its neutral connector is connected to ground, as that's how it's designed. If it tried to ground to the hot wire, it would fail to trip the fuse/circuit breaker.