So this is actually a post about the Rape of Nanking? The title is a bit misleading.
The only reason the Rape of Nanking is so alarming to people is that it happened fairly recently, and with a culture "civilized" enough that it scares us. Atrocities like this continue to happen in Africa even today but it's a lot more dismissable because we don't think of those places as reflecting on the civilized world. They don't worry us the same way subconsciously.
If you go back into history, the events at Nanking are nothing special. The Chinese themselves have done far, far worse, and to their own people. They have an incredibly long history of massacres and torture. Isn't Chairman Mao credited with tens of millions of deaths, including mass starvation and torture? There were Emperors who had zero regard for human life.
History is full of cruelty, but it just doesn't bother people the same way. I think it makes people worry about themselves and their own society when something like this is done by people they consider closer to their own level of civilization. They feel more ashamed of their own species than if it's done by some backwater dictator in a country they can't pronounce.
As far as human cruelty itself, there are different reasons, but it's usually related to power somehow. It's a way to reinforce power, both to the one in control and to those suffering. It's a way to feel superior and to push the other parties into an inferior level, to dehumanize them. Cruelty also has a long history of being used as a psychological weapon, to terrify enemies. Some people will do anything for power.
