The irony of human psychology
Human psychology is what we have to experience the world with. It's all we've got, in a certain respect. But for Nietzsche, it's a bad, knee-jerk response to the problem of consciousness. It's no different than animal psychology, thinks Nietzsche, except that it's more complicated and more social than certain animals. The major irony is that we trust our minds, but Nietzsche does not.
The problem of nature
Again, Nietzsche views humans as animals by nature (what else would we be? If Nietzsche doesn't believe in God, why would he believe in the divinity of man?). If that is the case, his argument is simply that "good and evil" should be built into us according our instincts. The problem is that humans also experience a sense of morality, but Nietzsche says we've confused ourselves with this religious language. He says the true "nature of man" is the same as the "nature of animals:" Survival of the fittest.
The irony of morality
Look at the popular notion of "Good." When Nietzsche started paying attention, he noticed that weak, helpless people always define "Goodness" as serving the needs of the needy. In other words, morality has been shaped in a way that prevents humans from completely overpowering one another. But if there is no objective standard (because Nietzsche is a nihilism, remember), then there is simply no reason not to let people do whatever they want, and let nature itself sort it out.
The irony of existence
Even Nietzsche cannot begin to speculate how anything exists at all. Rather, he faces the typical human idea of existence and he questions it. That's a common misconception about this book: Nietzsche is not saying that "good and bad" don't exist, but rather, he's saying that historically, stupid, weak people have shaped our ability to know what those words mean. The irony of reality is that people get what they get, with or without an additional "social morality."
The irony of community
People are born to live in community. That's how we've been programmed by nature, so much so that if you leave a baby alone, the child will die of exposure, even if its needs are provided for. So morality is necessary, then because humans have a social element, right? Wrong. Nietzsche's view is that even in light of community, humans are already programmed to be successful even without religion or morality. This serves his greater point that religious "Good" is really just weakness.
