If you really think you're fighting evil in a war for global domination, it's easy to justify to yourself that it's important you have the weapons before they do. Even if you don't think you're fighting evil; you'd still want to develop the weapons before your enemies so it won't be used against you and threaten your way of life.
I'm not taking a stance here, but it's easy to see why many Americans believed developing the atomic bomb was a net positive at least for Americans, and depending on how you interpret it even the world.
In this note: HIGHLY recommend “Rigor of Angels”, which (in part) details Heisenbergs life and his moral qualms about building a bomb. He just wanted to be left alone and perfect his science, and it’s really interesting to see how such a laudable motivation can be turned to such deplorable, unforgivable (IMO) ends.
Long story short they claim they thought the bomb was impossible, but it was still a large matter of concern for him as he worked on nuclear power. The most interesting tidbit was that Heisenberg was in a small way responsible for (west) Germany’s ongoing ban on nuclear weapons, which is a slight redemption arc.
Heisenberg makes you think, doesn't he? As the developer of Hitler's bomb, which never was a realistic thing to begin with, he never employed slave labour for example. Nor was any of his stuff used during warfare. And still, he is seen by some as some tragic figure, at worst as man behind Hitler's bomb.
Wernher vin Braun on the other hand got lauded for his contribution to space exploration. His development of the V2 and his use of slave labour in building them was somehow just a minor disgression for the, ultimately under US leadership, greater good.
I'm not taking a stance here, but it's easy to see why many Americans believed developing the atomic bomb was a net positive at least for Americans, and depending on how you interpret it even the world.