how and why does the neutral only carry the imbalance. 

Have you seen the physics maze experiments that show most of the time current flow will choose the shortest (least resistant) path to complete the circuit regardless of the polarity? Its mind blowing to actually see what is occurring. It may be time to adjust your explanation to suit the experimental results.

If an appliance needs 240V but the voltage is divided into 120V on each side, isn't it getting half the voltage it needs? Thank you