Why the neutral current is zero in WYE configuration in balanced load while it is unbalanced?

In a WYE 4 wire system the neutral, in theory, carries only the difference of current flow between the 3 phase conductors. So, when the current in phase A, B and C are equal, then there3 is no current flow in the neutral. When current flow in phase A only increases, then the neutral current will equal that increase.
However this is true only for purely resistive (linear) loads. Non-linear loads cause harmonics , some of which will add up on the neutral.

Because when you add all the currents together at the neutral they add up to 0 if they are balanced. If your balanced current was 10A/ phase then you would add 10cos(0) + 10cos(-120)+10cos(120) = 0 for a 3 phase system. If it's not balanced then when you add them all together you will have some current at some angle left over.