1. Derivatives can be riskier than the underlying asset.
2. Ratings agencies will lie if it makes a big client happy.
I don't think either 1 or 2 is controversial. And put together, those two truths will lead us right back to 2008.
I.e. if you have 2 independent bonds which will default with 50% probability you can combine 4 outcomes into a single one and issue two tranches.
The senior one should be payed back 3 times out of 4 (it's enough if one bond pays back) and the other will be paying back 1 time out of 4 (both need to work out).
But if the underlying things are correlated, they will fail or succeed at the same time, so when you buy the senior tranche your assumption that it's safer is wrong.
OTOH, buying the other one you'd get a good deal: you will pay for 25% chance of getting the money, but get something more than that.
Here is an old paper from 2001 that talks about how ratings agencies were using this math: https://www.jstor.org/stable/4480294?seq=1
The devil is in the details - even if you understand the math, you have a lot of choices to make. Ultimately you are going to have to set parameters on your model where the data to estimate the parameter accurately doesn’t exist. And at that point, math suddenly turns into opinion.
Understanding the probability bit explains that the trick depends on different modeling, not just on repackaging.