The bank liquidity ratio means that the bank can lend more money than it has to repay. In order to lend you €1,000 it must have €1,000. However the banking system only needs to have €300 (assuming a liquity ratio of 30% has been imposed by the central bank)
Bank of Ireland or AIB do not print money any more. The central bank does. Traditionally money was precious metal and its value depended on the metal it was made out of. Therefore a silver dollar was worth less than a gold soverign.
As banking systems evolved rather than carrying around a gold bar in your pocket to buy something you gave the gold bar to the bank and they gave you a note to say you had a gold bar. If the bank was minding €1,000 worth of gold in its vault it would issue notes and coins to the value of €1,000.
The banks then worked out that the owners of the €1,000 in gold were not all going to arrive into the bank on the one day and look for their gold back. Therefore the bank issued more bank notes. So it went and printed another €2,000 in notes and loaned them out to its customers. Now it was paying interest on €1,000 but was charging interest on €3,000 and making good profits. The difference between the rate it was paying out and what it was charging on the loans became acidemic, it could pay the same interest to deposit holders as it was charging borrowers and still make money.
Your point in relation to borrowing €1,000 from your bank is valid. The bank does have a coresponding liability for each asset. The banks make the profits they do because the banking system has more money in circulation than deposits or assets.
This is how you got a "run on the bank". People know that the bank had less money in the safe than it had loaned out and if you didn't get to the top of the queue to get your cash then you were goingto be left with nothing.
The banking system makes the money, the individual banks just slice up the cake between them.
Apologies if the post came accross as a bit simplisitc.