I don't know how to argue with very popular myth that states print money out of thin air ...

The government does not really "print money". Most of the money used in the monetary system appears through the process of issuing bank loans. The government is responsible for the physical appearance of banknotes and coins. This form of money exists to facilitate the use of bank accounts. They are distributed through the banking system, as bank customers need this form of money.

Perhaps the argument for you may be the fact that the US for example has a huge debt of 20 trillion dollars. If they can just print money "Out Of Nothing", where could the debt come from?