They bought into Nietzsche’s views on no God, no morality, and the idea of the ubermensch (superman) and therefore as intellectually superior and above everyone else, they had the “right” to do anything they desired - they could create their own morality.
Bingo! They were nihilists and the models for later generations. You can see the same themes in Crime and Punishment by Dostoevsky. The crime most similar to this was the kidnapping and murder of the Greenlease boy in Kansas City. in fact, the Frank kidnapping may have inspired elements of the Greenlease crime in the early 50’s.