But they can loan money that they don't actually have deposited....
Technically, they can only loan from the deposits, or possibly if the bank borrows from somewhere. If the bank has no deposits, it can’t loan. With fractional reserve banking, the banks loan out a certain percentage of deposits, but also keep that money on the accounts of the depositors. (That’s where the increase comes from... I have all my money, by 90% has been loaned out as well...)
You are on pretty good footing if you say that banks, through FRB, cause a growth in the money supply. You can’t say they just print money or increase an account balance and then loan it out.
Now whether you want to argue if FRB is fraud or not, that’s a different story. (How can I have my money and yet someone else has it too?)
If you are willing to burn an hour, this lecture is pretty good. Notice Salerno doesn’t make value judgements on FRB. Rather, he just lays out what it is and gives examples: