How do you explain economical crisis ( 2008 - 2012) to a layman?

When a bank decides to buy a loan, there is an agency that says how risky the loan is, based on how likely it estimates that the loan is to be repayed. The assumption that the rating agencies made in order to calculate the risk is that loans are independent, meaning if you have 100 loans, and each one has a 50% chance to be repayed, then the chance of all the loans not getting paid back is 1/2^100, so that almost surely you will get at least 30% of the loans paid back, and most likely 50% of the loans.

This type of rating allowed banks to give home loans to whoever they wanted, without worrying about the ability of the person to pay it back, because they could put the riskiest loans together with other loans, so that they looked safe, because, what's the chance of all these loans failing at the same time?

But Goldman Sachs people knew that these weren't safe at all, they were just being misrated by the rating agency. The reason is that a lot of these loans were taken as the prices of real estate were very high, and if the prices would go down, it would make no sense to pay a loan which is worth more than the collateral, you would be better off just letting the bank take the house, and then buy it again at the new cheaper price. So if housing prices were to go down, ALL the loans would fail, and it wouldn't be a coincidence.

But then, instead of alerting the agencies to the rating issue, Goldman Sachs got these loans, went to AIG and said they wanted to take insurance against failure of these bundled loans, then they passed the loans on to other banks. The insurance would pay them back in case the loans would default. They figured they would make a ton of money, because they knew that those loans would fail when prices start going down. The insurance was cheap, because AIG was using the rating agency's estimates for the chance of failure of these loans, which was completely wrong.

But they weren't alone in doing this, a whole bunch of other financial people also realized this, and also went to AIG and bought insurance against failure of these loans. They were all thinking "boy, am I clever to have figured this out. When the loans fail, we're going to make a ton of money".

Then the loans failed, and AIG had to pay off all their insurance policies. But they had priced them too low, so they didn't have enough money to pay these off! Because they were using a wrong probability model, they never expected to have to pay so much. So AIG was going to fail, and then Goldman Sachs wouldn't get it's money. Those banks that were left holding the loans also were in a terrible situation, they were holding suddenly worthless assets that used to be worth billions of dollars.

But then instead of letting those firms go bankrupt, the government gave a ton of money to prop them up, by buying the crap loans. Instead of Goldman Sachs losing a ton of money when AIG failed, they made a ton of money. If the government had not stepped in, all these enormous financial firms would probably have collapsed, and I am not sure that this would be a bad thing.