In any undergraduate course on probability, one of the fundamental results that is discussed is the central limit theorem. Apart from the interesting mathematics needed to prove the result (most often introducing moment generating functions, and more subtly the idea that the distribution of a random variable $X$ can be characterized by expectations $E[f(X)]$ over a rich enough class of test functions $f$), the central limit theorem can be a good opportunity to teach students about the so-called universality of the Gaussian distribution.
That being said, I would like my explanation of universality to come with one very important caveat, so that my students do not, like many people, become "unreasonably enthusiastic" about the Gaussian distribution. (Essentially the error I would like them to avoid is what is explained in this answer to the question "Impressive common misleading interpretations in statistics to make students aware of".)
So my question would be as follows:
Question. Are there well-documented examples of people who, likely because they erroneously assumed some distribution to be Gaussian, were led to a catastrophic outcome? (Perhaps in the insurance or financial industries, or other.)
I feel that an interesting real-life example would help drive the point home that, if you want to argue something is Gaussian by invoking the CLT, you better be able to write it down as the sum of a large number of i.i.d. variables divided by square root of their number.