If you and your family have $250,000 or less in all of your deposit accounts at the same insured bank, you do not need to worry about your insurance coverage –your deposits are fully insured.
http://www.fdic.gov/news/news/financial/2008/fil08102a.html
What is FDIC’s role in a bank failure?
In the event of a bank failure, the FDIC acts in two capacities. First, as the insurer of the bank’s deposits, the FDIC pays insurance to the depositors up to the insurance limit. Second, the FDIC, as the “Receiver” of the failed bank, assumes the task of selling/collecting the assets of the failed bank and settling its debts, including claims for deposits in excess of the insured limit.
http://www.fdic.gov/consumers/banking/facts/index.html
I hope this lets you understand the FDIC's role a little bit. I think we have to go back to basic economics class first though, cause he's not understanding how the system works.
Okay, first off, what does it mean when a bank goes under? It means that the company part of the bank is running more than a certain level negative, I can't remember what level that they consider that, but you can look it up I'm sure. (Sorry, have a headache atm and not researching everything for you.)
Does this mean that they have no money? No, you still have money in the bank, the bank still has money in their vaults, it's just the administrative end that folded.
Why can't I pull out all of my money from a bank whenever I want? Well, this would depend on how much money you have in the bank and how many other people are pulling their money out. A bank is required to keep only a certain amount of cash on hand in their vaults because of secruity reasons. The money will be shipped to the Federal Reserve Bank and the bank will be given an IOU by them for the money. That's why you see armored trucks go by banks all the time, they're usually shipping money to or from the Federal Reserve Bank or from that branch to the bank's main branch office. Most of the transactions reguarding bank to bank transfer of funds is done electronically through the Federal Reserve Bank. Because of this there really isn't as much actual physical money in circulation as the total amount of depositors have put into banks.
What about loans? Well, banks are able to make loans off of a certain percentage of what their depositors have put into the bank. This number is defined based off of the normal yearly deposit and withdrawl amounts. These numbers are considered very carefully by a bank and are gauged to allow them the most profit and you the best interest on your deposit. The interest that you get from your bank is usually paid for by the loans that they give.
Why wouldn't banks going under directly affect the stock market? The stock market uses virtual currency called stocks. It is given a dynamic value based off of how well the company that issued the stocks is doing. When a company goes under people will pull their stocks out of the company and then invest in another company.
Why do bail outs affect the stock market? Well, let's say that you have stock in Company X. Company X is hitting rock bottom so people start pulling their money out. Suddenly the government steps in and decides to "bail out" Company X and give them a bunch of money so that they don't fold. The stock for Company X goes back up again as if by magic. When this happens too many times you'll have investors leave their money in there just to see if Company X is going to get bailed out or not.
The stock market is a completely separate thing from the banking system. As a matter of fact we could have no private banking system and the stock market wouldn't be affected. The stock for that particular bank would be worthless but it's the same as an electronics store or a telephone company going under, nothing more.
Hope this helps you to understand a little bit.