Answer:
Arguments for: We were at war and it was estimated that a million or more American servicemen would die (not to mention huge numbers of wounded) over the course of a multi-year invasion of the Japanese home islands, followed by a likely guerrilla resistance, if massive force was not used to get the Japanese to surrender. Years after the bombs were dropped, it was also suggested that fewer Japanese had died under the two bombs than would have died had there been a conventional invasion.
Arguments against: It was an inappropriate attack on civilian centers that had increased in population because those cities had not previously been bombed during the war. A demonstration on an uninhabited site to which the Japanese were invited in advance, should have been attempted first. (It was considered and thought to be impractical.) The atomic bomb was a new and terrible weapon and should not have been used. (Argued after the fact.)