First I will give the perspective of those who believe the bombing of Hiroshima and Nagasaki was indeed justified. Operation Downfall was the planned invasion of Japan but it would not be like any normal invasion. The American forces knew that they planned to confront provoked and zealous Japanese, which would cause skyrocketing casualties.
The majority of the forces believed in a concept referred to as bushido, which demands bravery and extreme self-sacrifice. Honor comes from death and disgrace from surrender, so those who willingly gave their lives were esteemed and respected. This belief stems from feudal Japanese samurai warriors but is still widely accepted as a motive for war. During World War II, when the Japanese air fleet was outdated, they developed a defense of kamikaze pilots which were basically suicide bombers. This showed the United States that when backed into a corner the Japanese were going to fight back with everything they had. It was estimated that invading Japan with a normal attack would cost 1.2 million casualties (Source #2, see annotation).
This was one of the most prevalent factors in President Trumans decision to authorize the use of the atomic bomb. The other leading influence on the atomic bombs justification was the Japanese