We must be the change we wish to see
Silence is one way of drawing a boundary. It is particularly useful when you do not want to engage in conflict or pursue a violent dialogue.
Many parents have difficulty disengaging from their children when they start to bicker and pout about a chore or house rule. Mom says: Time for the TV to go off. Child asks: Why now? Mom answers: Time to do your homework. Child replies: Just one more program...
You can explain the rule to your child and justify any points he takes issue with. This is especially appropriate when the rule is new or has not been well understood. You can also be flexible and negotiate with your child, especially if he is growing out of a rule and needs more autonomy. Generally speaking, however, a child needs rules and boundaries to be firm in order both to know where he stands with you as an authority, and to have some dependable guidelines for making his own decisions. To respond to his every objection, to allow every conversation to escalate into an argument, or to let your child harass and badger you into submission is simply allowing him to violate your boundaries. This is not good for either him or you.
You have the power to defuse this situation.
If your child already knows the rule, if he has had a reasonable explanation of it in the past and has been given fair warning about your expectations when the rule is broken, this may be the time to remind him of that, and then turn the TV off. If your child continues to argue with you, you may want to placate your child with empathy but, in terms of arguing anything, it may be best to remain silent.