Every time there is a significant natural disaster I eventually hear from someone that there is at least one upside: the disaster will be good for the economy. And every time I respond, "Wrong!" Inevitably this supposed economic stimulus is called a "sliver-lining." To quote on of my favorite demotivational thoughts from Despair.com, "Pessimism: Every dark cloud has a silver lining, but lightning kills hundreds of people each year who are trying to find it."
Natural disasters are bad. They destroy lives and wealth and that has no upside. After the disaster is over, people are unambiguously worse off than before and while their quality of life inevitably recovers, on average they are not better off in the long-run for having lived through the disaster.
Big shocks like disasters also have redistributive effects. When a large number of homes are destroyed, it may well be that previously underemployed construction workers end up better off. But in net their benefit is more that cancelled out by the loss to the rest of society.
The myth that disasters are good for the economy comes from a misunderstanding about what economic activity measures. The most commonly watched measure of economic activity is gross domestic product, or GDP. GDP measures the value of goods and services produced within a specified geographic area over a specified period of time. Roughly speaking GDP is equal to aggregate income, because the funds used to purchase these goods and services are funneled back to households in the form of wages, stock dividends, interest and rental income, small business profits.
However, GDP and income are not good measures of well-being. Economists use the term utility to refer to this. To see the that income is not utility consider the case of a retired worker with all his savings in the form of cash. This person has zero income, but if he is buying goods and services with his savings, clearly he is not as bad off as a homeless person who also has zero income. Perhaps wealth is a better measure of utility (though that has problems too).
When a disaster strikes it does spur GDP. People work to replace damaged homes and businesses and that will lead to an increase in income to workers and suppliers of building materials. However, wealth has been destroyed. The resources, time and effort that have been used to rebuild and raise GDP could have been used for some other useful purpose had the natural disaster not happened.
Like many things this is easier to see if you think of a small scale example that effects only your own household. If you wake up on Saturday morning and the storage shed in the backyard has collapsed, you will get to spend the day rebuilding it rather than watching college football. Your home production or GDP will have risen since you built or rebuilt a shed. But in the end you would have preferred to spend a leisurely Saturday watching TV. Your utility is lower even while GDP has risen.
One of the easiest ways to see that disasters are not good for the economy is to realize that they are easily simulated. We could replicate the effects of an earthquake or storm with well-placed explosives. No one seriously proposes blowing up otherwise useful property as a form of economic stimulus, however.
Ultimately the terminology we use is the best evidence. We call earthquakes, storms, hurricanes, floods, and wildfires "disasters" after all.