A qualitative approach - not a rigorous mathematical one:

If you really do switch precisely at the zero voltage point then, by definition, there is no current flowing (we are talking resistive loads here).

If you throw a switch that has no voltage across it and, therefore, no current flowing through it you are not actually changing anything at all! If nothing changes, there is nothing to raiate!

QED.

Of course, in practice, switching takes a finite time: so there will be a finite voltage across the switch and a finite current through it during the switching process - so there will be some radiation.
But all this takes place in a very tiny timespan and, because it is all still close to the zero point, the currents and voltages are all still very small - close to zero.
We can thus say that there is next to no voltage across the switch, and next to no current through it - so we get next to no radiation!