The war went more like this:
We demanded surrender or the Japanese would face total annihilation. They refused.
We dropped a nuke on Hiroshima, asked for them to surrender unconditionally again. They refused again, and made no comments about the emperor, yet.
We bombed Nagasaki, the Japanese refused to unconditionally surrender. Their only term: The Emperor was left unarmed and in power.
We gave into that demand. Which saved the lives of millions of Japanese and Americans and ended the war.
Instant death by nuclear bomb is a lot more humane that dropping thousands of incendiary bombs and burning a bunch of people to death.
All of the arguements against the nuclear attacks hinge on maybes. Maybe the Japanese would have surrendered without us blowing up two cities. The truth is probably not. I like to go with factual historical evidence instead of the hearsay of "Japanese officials" who would probably like nothing more than to make the US look bad.