Answer:
What finally persuaded President Truman to use the atomic bomb on Japan was that it seemed that the Japanese would never surrender, no matter how badly they were beaten back.
Explanation:
By mid-1945, the Pacific War was at a turning point. The American forces were defeated to the Japanese Army, obtaining victories in the confrontations and getting closer and closer to the Japanese territory.
Although the Japanese defeat was imminent, the Japanese defended their territory until the last consequences, literally. For example, in the Battle of Okinawa, Japanese casualties exceeded 100,000 deaths out of a total of 110,000 men. The Japanese fought until the end, implying a large number of American casualties.
Therefore, President Truman made the decision to launch the atomic bombs in Hiroshima and Nagasaki in order to force the Japanese surrender without implying a great loss of American lives, as an invasion to Japan would have implied.