Do you think the U.S. Gov creates new currency?
The U.S. Gov doesn't create new currency either; it also borrows it.
It also doesn't borrow it from the Federal Reserve Bank; it borrows it from private lenders.
Does this surprise you?
People regularly talk about the U.S. Government printing currency, even though they do not; likewise I'm referring to the Greek govt printing currency, even though they do not. It's a concept which works well to explain what's happening for the average person. I don't think I would've got down-voted if I'd said that the U.S. gov prints money, even though they get new money the same way that Greece does.
If you're going to expect me to describe the full details of what is happening in Greece, then you should expect the same when people talk about the U.S.A.
When a government wants money, it offers up government bonds, and at the same time gets its regional central bank (if it has sufficient influence over them which it usually does) to offer reserves to commercial banks at a slightly lower rate than the rate they're offering for their bonds. So, this leads the commercial banks to take out the reserves in order to buy the bonds (creating new deposits in their ledgers in the U.S. government's name). In this way, the government is effectively creating (which we still call printing even though it's mostly digital) its own money for a very cheap rate. This is why the governments are in debt, even the U.S.A, because they are not actually creating their own money directly.
This is monetary inflation (as opposed to price inflation), this is new money coming into existence as a result of the government's actions, this is devaluing the money of the populace and transferring the wealth to itself, by its promise to collect taxes from those same people in the future in order to repay the private creditors. It's not really right to call it borrowing and loaning; it's crediting and debting. The money which is being 'borrowed' did not exist prior to it being 'lent'.
When the Greek Central Bank wants to create new reserves (which it does in response to demand from commercial banks, which is turn commercial banks do in response to their customers), it just has to ask the European Central Bank for some reserves, to which the ECB automatically obliges. The ECB doesn't debate over whether to grant reserves, all it does is set the interest rate and than creates them according to demand. So there is really no difference between how the Greek government creates new money and how the U.S. government creates new money. They both 'print money', by the obfuscatory concept.
With Bitcoin... New Bitcoin cannot be created as credit.
Hopefully you can see, now that I have explained a small amount of how the banking system works, how it would be quite different if people were holding Bitcoins. There is other wisdom you must possess in order to understand why this is the case, e.g. that value is subjective, and the Euro is only valuable to the degree that people want to hold it. If people would rather hold BTC, then EURO is less valuable, and the people holding the BTC do not have their BTC devalued by the printing of EURO, and the govt can't print BTC itself...