Question

What arguments did Truman consider when deciding whether to use the atomic bomb?

Answer 1

He wanted a quick and easy finish to the war against Japan. 
He wanted to save/prevent the loss of as many American lives as he could. 
He wanted the war to end before the USSR became involved. If the USSR came to aid the US, they would possibly want some territorial gain after the war ended. Truman wanted to avoid this. 
It is possible that Truman wanted to show off the power of the United States with the dropping of the bomb. By being the first to use an Atomic Bomb, America would become superior to the USSR and other countries around the world and increase their world status. 
He also thought it would be the only way to guarantee the end of the war with Japanese unconditional surrender.