Why does reducing pressure cause the equilibrium to shift towards the side with less moles?
Actually, the shift of reaction towards left on decreasing pressure (and towards right on increasing pressure) is due to Le Chatelier's Principle, which states that if a change is brought in the equilibrium conditions of a reaction, the reaction will proceed in such a manner that it counteracts the change.

In case of increasing pressure the reaction shifts to right due to lesser number of moles on right. And according to gas equation, lesser moles means lesser pressure. The opposite happens when the pressure is decreased.