The Supreme Court, in its infinite wisdom, has ruled that you cannot exercise your right to remain silent by merely remaining silent, and that the Prosecution can say things like "you didn't have an answer when asked questions".
To exercise your right to remain silent, the Court says, you must say "I am exercising my right to remain silent".
And don't say "I want a lawyer, dawg", or else the police will say they were unable to find you a canine who had passed the bar, and thus your request for counsel was not a serious one and that they are free to continue your interrogation... and the Court (in this case, the Louisiana Supreme Court) will say that that was a perfectly reasonable interpretation of your request.