Maybe. Maybe the bank needs to increase its reserves instead. The handwaving is in saying that "money will usually end up going this way" as if it's the only relevant possibility.
It's well understood throughout business that, when determining how much something is worth, you have to subtract out obligations. So I don't see how you can say that money is being created. What happens is that the use of money is allocated over time. Borrowers can use it, and what they are able to buy with it, while depositors don't. They aren't using the same money at the same time.
I start with a blank economic system. Fractional reserve rate 10%, $1,000 in system.
John Q puts $1,000 in a bank. Charley G company takes out a $900 loan. They use it to build a business, which sells widgets.
I have $1,000. The Charley G company has $900. The bank has $100.
Charley G invests in many things, and makes a decent profit. He gives the profit to his employees, who put it in a bank, or spend it (giving to Paul F or Nancy C or something). This puts $900 eventually into a bank (if not through the employees, through the corporations they are purchasing from.
The bank lends out $810 to Ron W corp.
At this point, there has been $1710 dollars of capital investment from the $1,000 deposit. This $1710 has gone into two loans, which were used to build Charley G and Ron W's business. These businesses are permanent economic features, and are capable of generating a more revenue. The economy gained $1710 of value from these two stores ($900 in value from the Charley G store, $810 in value from the Ron W store).
That's a significant economic gain, right there. Charley G has built a $900 business, Ron W has built a $810 business.
That growth would have been impossible without the bank. The best John Q could have done was take his $1,000 and invest it in a business, which would have created $1,000 in economic value to the community. Therefore $1710 of economic dollars (value) exist, and $1,000 was the initial input. $710 in value has been created.
Now imagine that John Q walks into the bank and asks for $1,000?
The banks have $1710 in outstanding debt, but only $190 cash on hand (two inputs). They need $810 quick. That's not a big deal, right? They have $1710 outstanding debt, they need less than half back.
They call up Ron W and Charley G for $400 each from the loan back. Charley G is a responsible business man, he cuts 2 employees, and comes up with the $400. Only now the two employees need their money. They go in and ask the bank for their money - they are out of work, they need it.
The bank just scrambled together $1,000. They need to call in more debt for, say, $300 for these employees. They call up Charley G and Ron W.
Ron W can't absorb this. He's out of business. Now his employees need their money back. Also, Charley G is nearly dead.
This run has collapsed one business and nearly killed another. Now people get worried. They want their money before the banks can't scramble hard enough to find it. They all run into the bank.
Money creation - its advantages and costs.