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.