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Unfortunately, it made sense given the context.
The U.S. had been firebombing strategic targets in Japan for 6 straight months, but despite this, the Japanese absolutely refused to surrender. The choice, then, was to either invade the island or to use weapons powerful enough to force the Japanese would surrender.
Given that Operation Downfall, the projected invasion plans, had a projected casualty rate of nearly 500,000 American soldiers killed or missing, and the fact that the U.S. believed (in hindsight, correctly) that Japan's defense relied on making the invasion too costly to support, Truman chose to do the latter.
I don't have the numbers on me, but even with cancer deaths factored in, the casualties of the bomb attacks were lower than Downfall's projected casualties. Of course, it Japan hadn't surrendered after two attacks, this might not have held true (not that the U.S. had any more completed bombs at the time, but several more were in production and would be ready for deployment over the coming months, with Deadfall planned for October if the Japanese still refused).
It was a gamble, but ultimately, it's one that I have to support, but only with sadness. Really, I don't see that the United States had many options to work with at the time.
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