Statist claim: Only the government can do X.

Fallacy:

If the government is not doing something about a problem, then nothing can be done about it. Only the government can solve society's problems.

Response:

Virtually every problem can be handled better and more morally by voluntary action than by government aggression. Most statists are unaware of how the issues have been addressed historically without State intervention. Money, law enforcement, courts, benevolence for the poor, health care, and yes building the roads has all been done by various societies before the modern State captured and monopolized these services. [HB]

This is called the Fallacy of Government Solipotence, or alternatively the Barefoot Fallacy.

"If government didn't exercise control over the manufacture, distribution, price and sale of shoes we would all go barefoot!"

If "shoes" doesn't suit you, just substitute "police" or "fire protection" or "mail delivery" or anything else the government claims to provide. Nothing the government claims to provide cannot be provided in a more humane, just, and economical manner by free associations of individual people.