Why is it said that a typical 120V household circuit "reverses" polarity?
My previous answer was a bit unclear, and a bit misleading. So I'm going to take another stab at it.

As before, we'll start by looking at the secondary side of a single split-phase transformer. And again, the loads are represented by purple rectangles.



Then we'll spit the circuit up into individual circuits, so we can take a closer look at each circuit.



If we visualize the current flowing through the circuits in the first 60th of a second, the current will flow like this.



During the next 60th of a second, the current will flow the opposite way.



The interesting thing about this, however, is if you look at the current flow on the neutral.  When you overlay the images, you'll see that the current flows both ways simultaneously on the neutral.

 

Because of science, the opposing forces cancel each other out. However, if one force is larger than the other, the current will not be completely cancelled out. So the "unbalanced" current will flow on the neutral, in whichever direction it's flowing during that cycle.

So technically, you could say the current is flowing both ways, and neither way (if they completely balance) at the same time. 



Extra Credit

Facts


Neutral is always "0" volts.  
L1 and L2 cycle from positive volts, to negative volts (alternately). 
Energy always flows from points of higher potential, to points of lower potential.


Therefore...

When L1 is greater than "0" volts, current flows from L1 to N.  When L1 is less than "0" volts, current flows from N to L1.  

When L2 is greater than "0" volts, current flows from L2 to N.  When L2 is less than "0" volts, current flows from N to L2.  

When L1 is at a higher potential than L2, current flows from L1 to L2.  When L1 is at a lower potential than L2, current flows from L2 to L1.