Please explain bank runs to me

For a bank, the loans that it lends out (i.e. mortgages, car loans, etc.) are treated as assets, and the bank makes revenues from this.
On the other hand, when a bank has interest-bearning depositors there, the bank must pay these savers money in the form of interest payments. This is a liability, and it's also a cost of doing business.
The interest-bearing deposits are netted to the revenue streams from lending activities, and the difference is the gross income, pretty much.
I realize that the different assets that a bank has lended against is weighted, according to Basel. Money markets and governmental securities are weighted at 0.0, and stocks are weighted much higher.
However, why can't a bank simply lend out money and not worry about deposits, since it is the depositors that are draining the bank of revenues?
Lastly, I suppose that a bank would have $100 in interest-bearing accounts earning 1%. They would lend out $1000 at 6%, and the bank would pocket the difference.
Suppose that all the investors (or the depositors in interest-bearing accounts) all of a sudden took their money out of the banks, it's not apparent to me how the bank would lose a lot of money. This, by the way, is a bank run. I would think that a bank with very few liabilities, AND good borrowers is a very good business model.
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