Why would an exchange need to borrow money from you to allow transactions?
Both parties of the transaction send their money to the exchange before the transaction takes place. That means the exchange actually has excess (working) capital.
The reasoning I understood was to provide liquidity of currencies, not money in general.
So if I want to sell my ABC token for XYZ token, they are borrowing your XYZ token that you have gaining interest to make the transaction work. They are then taking the ABC token I sold to credit an ABC token they had borrowed from someone else.
I may be completely wrong on this but that was my understanding of why this worked. Of course it doesn't work when everyone wants to take their money out. I would assume a responsible entity would use the money earned from fees to help provide liquidity.
I would also assume a responsible entity would want to stop transactions of ABC token if there was no longer enough liquidity to support the above borrowing & trading.
Both parties of the transaction send their money to the exchange before the transaction takes place. That means the exchange actually has excess (working) capital.