Your diagrams are not telling us what you want them to tell us. Indeed, you just lost the argument that you were trying to make. It comes from the fact that in the top diagram, X and Y are equal, so X-Y gives you zero. But in the bottom diagram, X turns out to be two times Y, so X-Y is not zero. Please let me explain.
Let us assign values to the resistances in both diagrams, such that each load has a current of 10 amps. So in the upper diagram, you have 10 amps flowing in the top wire (L1), so X =10. You also have 10 amps flowing in the bottom wire (L2), so Y = 10. In the center wire (N), the current is therefore zero (10 ? 10). That is indeed what you get, when loads are balanced in a 120/240V single phase system, such as the one you have drawn.
? Top diagram summary: Three wires, one with 10 amps, another with 10 amps, the third with 0 amps.
Now look at the bottom diagram. You have 10 amps flowing through the left hand switch, so the thing you labeled ?X-Y? has a current of 10. You also have 10 amps flowing through the right hand switch, so the thing you labeled ?Y? has a current of 10. That means that the current in the top wire (L1) must have a current of 20.
? Bottom diagram summary: Three wires, one with 10 amps, another with 10 amps, the third with 20 amps.
I would easily accept the top diagram as including only two current-carrying conductors. But the bottom diagram clearly has three current-carrying conductors.