Religious assumption
Although many people feel properly atheistic during Nietzsche's time, that doesn't stop him from turning his critical eye toward both free thinkers and religious people both. In "The Parable of the Madman," Nietzsche criticizes atheists who forget to completely abandoned their religious assumptions. In "Beyond Good and Evil," he explains the silent religious assumptions that people tend to accept without questioning.
The Anti-Christ irony
Of course, at the end of the 19th century, there were the beginnings of free thinking, but Nietzsche played a major role in that. These writings include his ironically oriented essay, "The Anti-Christ," where he elaborates the vices of Christianity, the way Christianity seems to protect weak and incompetent people, and he paints mercy and charity as vices, asserting that the will to succeed was the true virtue.
Sociopathy and irony
Although Nietzsche is technically sociopathic, meaning that he abandons the moral assumptions of his community, he takes that to ironic lengths. He explains how in an ideal state, the nature of man would involve violence, aggression, domination, competition, and frequent death. Ironically, he isn't just making use of sociopathic ideas—he is advocating a full-blown rejection of morality, especially in "Beyond Good and Evil," and "Thus Spoke Zarathustra."
The irony of happiness
In the essay, "The Gay Science," Nietzsche writes philosophy that would unnerve anyone who wanted to read it for the title's promise of happiness. In fact, the whole reader seems ironically predicated on the reversal of happiness. Instead of orienting his ideas around happiness as the ultimate goal, he makes his ultimate goal skepticism, and he figures out that by accepting the game of happiness, many people have started believing things that are not true. He has a low opinion of this emotional approach to philosophy.
Death as a kind of irony
Nietzsche writes about death openly, bringing it into the forefront of his thoughts. He writes in "Ecce Homo," about mankind, about man's aversion to death, and about the hysterical short-comings of modern philosophy, which often seeks to understand the world without addressing the horror of human death. He especially hates when religions remove the question entirely by suggesting that death is only an illusion.
