You address an important issue that many experts believe will haunt our economy in the coming years. To further answer your initial question:

Why are banks willing to lend money to people who cannot afford to pay them back?

One of the reasons that the recent addition of mortgages as commodities to be bought and sold on the market. The company that provides the loan to home buyer does not have any incentive to care if the home buyer is able to pay back the loan. If the plan is to sell the mortgage to someone else, the lender can just immediately cash in on the market value of the loan and move on. They pass the burden on to someone else, like a game of hot potato. This game of mortgage hot potato is what has been happening throughout the recent housing boom and someone will eventually get burned.

You address an important issue that many experts believe will haunt our economy in the coming years. To further answer your initial question:

Why are banks willing to lend money to people who cannot afford to pay them back?

One of the reasons that the recent addition of mortgages as commodities to be bought and sold on the market. The company that provides the loan to home buyer does not have any incentive to care if the home buyer is able to pay back the loan. If the plan is to sell the mortgage to someone else, the lender can just immediately cash in on the market value of the loan and move on. They pass the burden on to someone else, like a game of hot potato. This game of mortgage hot potato is what has been happening throughout the recent housing boom and someone will eventually get burned.