When a country make too many of their currencies, it will eventually lower the currencies' value and inflation would occur.
But why won't key currency work like this? If the US is making more and more money, shouldn't the value get lowered at some point? Where did all that amount of money which has been coming out of US go? Is it because the world is still growing even now, and the circulation needs more and more Dollars constantly?
The demand for a key currency, like the USD - in contrast with other national currencies - is based not only on the domestic economy, but the global word economy. As the USA is viewed as a superpower and a global leader in economy, accordingly the US currency is generally viewed as a stable monetary asset which can be used as a global currency in international trade, or a clearing unit in international transfers and a value safeguard.
Some other currencies are tied to the value of the USD as well, which makes global trade much more calculable. As a result of this collective perception, the demand does not depend that much on the US economy, but the global economy and other global processes. This is obviously beneficial for the US economy and government as well, as it has much more wiggle room in becoming burdened with debts, while able to keep the value of its currency.
Additionally, I would proceed with caution on the belief that just printing money causes inflation. It is not just money printing but money velocity. You can print your heart out like Japan has done for the past couple of decades and unless everyone is rushing to get rid of the currency via purchases of some sort, then you don't really have a lot of velocity and you will not get much inflation.
Again, Japan has been printing its heart out with their yen and for the past two decades they have been experiencing deflation, not inflation.