The answer to this is simple. If you change gear w/o stepping on
the clutch, you are "forcing" the transmission shaft to change
gear. Either u will hear a horrible sound from your gear box or
your car will simply stall.
Therefore, if you change to neutral w/o stepping on the clutch,
your transmission shaft will be disconnected from the gears as
usual. You wont hear any sound also since you're not forcing a gear
change. However, you are still forcing the disengagment of gears.
This is bad for the gear box.