Do the donated NFL losing team shirts destroy local economies? I've recently become aware of the fact that the NFL prints both championship teams' shirts in advance to satiate incredible demand -- but instead of destroying the losing teams' shirts like they used to, they instead donate them to developing countries. But the thought of flooding these local economies with free shirts, which doesn't create jobs, GDP, and hurts local clothing business, seems like it would be terrible for the economy. Is this indeed the case?
My answer is no, it doesn't hurt the local economy. This seems like an example of the "Broken Window Fallacy":

Suppose, when nobody is looking, I break all of the windows in my neighbour's house. This creates a bunch of work for a glazier who might otherwise have been idle. So it seems like, by going round smashing things up we can provide a boost to the economy. Surely this must be wrong!?

Indeed, the problem with this logic is that we have to think what would happen if I had not broken the windows. My neighbour, not having to incur the expense of replacing his windows, would have some extra money to spend on a hair cut or a new bicycle, creating work for a barber or a bicycle maker. If the windows are broken then those guys miss out.

So the glazier earns some extra income and gains; the barber earns less income and looses. But these two things "cancel out": this is just a transfer of wealth from one person to another rather than the creation of new wealth. My neighbour, on the other hand, definitely loses because he doesn't get a hair cut any more. So overall, the broken windows are a net loss to society.



The reason I think this is relevant to your question is that we could reframe it as: "if we burnt the shirts [broke the windows] instead of giving them away for free, wouldn't that create work for a tailor and therefore make society richer?"

I think the answer is no because, freed from the need to buy a shirt, people have more income to spend on food, educating their child, taking care of their health, etc. All of these things create jobs in the local economy to replace the lost jobs in the clothing industry.

It is true that the tailors lose out at the expense of the farmer, teacher, or nurse. But over long time horizons people will adjust to this by training to do the jobs that pay. 



tldr; Destroying real resources may create winners and losers, but is almost always bad for society overall.