I found this Wired article [0] to be a good start behind what actually happened in the math. The problem was not that subprime loans were being made. The problem was that bundles of those subprime loans were being tranched and sold as high-quality investments, even though none of the underlying assets were anywhere close to high-quality.

And all of this was foreseen by people who actually understood the math. And they were promptly ignored because listening equated with lost profit, commissions, etc.

[0] https://www.wired.com/2009/02/wp-quant/