Current flow in AC circuits

What drives the current through the load is a difference in potentials (potential difference or voltage) between one end of the load and the other. Compare this with the flow of liquid through a pipe being due to a pressure difference between the ends of the pipe.

On both halves of the cycle there is a pd across the load. On one half cycle the neutral is at a lower potential than the live; on the other half the neutral is at a higher potential than the live. So, either way, there will be a current.

The only reason that the neutral is called 'neutral' is that it is connected to the ground, or at least close to ground potential, meaning that if you are standing on the ground with poorly insulating shoes and touch the neutral wire, it should not be life-threatening, but NEVER DO IT - there can be mistakes.

If you have a tank of water sitting on the ground, does water flow into it or out of it?

It depends on what the alternatives are. If you have water at a higher gravitational potential (like up on a table), then water will flow from the one on the table to the one on the ground.

If you have a tank down in the basement, then water will flow from the tank on the ground to the one in the basement.

The same is true for the wires in your circuit. The fact that one of the wires has a voltage that is called 0 is just a convenience. All that matters for the circuit is what the difference is between the wires.

Electrons will flow from the lower potential to the higher potential. Sometimes the "line" or "live" wire is above the neutral/reference potential and sometimes it is below it. So charge will tend to flow in opposite directions during the two portions of the cycle.