The main rationales behind the government’s control of the money supply are that A) the money supply is so important for the country’s economy and B) that private banks might pursue their own interests instead of those of the economy as a whole if they were left in charge of the money supply.
The money supply is extremely important to the economy of a country. If there is not enough money, the economy will have a hard time growing. If there is too much money, it will “overheat” and inflation will result. In either case, poor control of the money supply can lead to very negative economic consequences. Because the money supply can have such an important effect on the country as a whole, governments tend to want to control that supply.
They also wish to control the money supply because they, unlike individual banks, have a huge stake in the performance of the economy as a whole. Individual banks would be more concerned with their own finances that with the overall performance of the macroeconomy. This could lead them to make decisions about the money supply that would help them, but would hurt the country.
Thus, the rationale for government control is that the money supply is very important to the overall economy and cannot be entrusted to banks who would have mixed incentives for changing the supply.