Why do we have "live" and "neutral" wires?
You are right. Current flows from neutral to life every 1/30 of a second (1/25 here in Europe). You can think of it this way:
During a positive half cycle live wire "pushes" current (note the quotes) to the neutral wire trough the connected circuit (fridge, washing machine, etc.)
During a negative half cycle live wire "pulls" current (again note the quotes) to the neutral wire trough the connected circuit.
In either case work is done when the current flows.