The silent treatment gives a feeling of power and influence over you to your child. It's how they push your buttons and make you leave your buttons behind.
Know that this is possibly the best problem-solving ability he has at that moment if your child gives you silent treatment. Simply put, by using this passive-aggressive behaviour, he's trying to deal with whatever problem is at hand. And he has found a way of getting the upper hand by withholding information or thoughts.
The hard part for parents is that the more you make a problem of it and the more painful or irritating you behave, the more it will be used by your child to get to you. And the less likely your child would be to learn more suitable ways of addressing their problems.
Indeed, in relationships later in life, this form of passive-aggressive conduct is very destructive. This is a pattern that you don't want your child to give in to and reward you.