The Evil of Moralism
When Nietzsche expresses a disdain for moralism, he is referencing the argument he seeks to undo in the second section of the book by asserting that 'good' is power and 'evil' is weakness. Anything outside of those paradigms is strictly unnatural and manipulative. This is doubly true for the idea of Christian morality which posits that the highest good is self-sacrifice, just like Jesus died to atone the sins of the human race, and the highest evil is esteem yourself to be most valuable than others, which in the Christian schema is called pride.
Even for modern day theists, this criticism is enlightening. What Nietzsche accomplishes by tangent is explaining how modern moralism is an extension of theism alone, and if one believes that there is no god, then the fabric of morality itself is lost as a logical consequence. Nietzsche offers the naturalistic, animalian view of morality in the place of the religious view. Good is simply what you can accomplish for yourself through the use of power. Evil is when you can't do what you want because you're weak and pitiful.
The Falsity of Judeo-Christian Texts
Previously in Europe, religion had been regarded as a given, something that was not truly available for public criticism. And then, in the 19th century, after the Enlightenment, there was suddenly room for skeptics to argue against religion as a system, which Nietzsche did as a sort of atheistic prophet.
His argument is seen clearly in this book, that religion is a device that benefits those who aren't able to protect themselves from power. He takes time in the Antichrist to explain how the story might have developed over the course of many years for the purpose of establishing cultural and legal perspectives that would limit the ability of the powerful to exert themselves over the weak at their expense. How could they achieve that in a society that had to answer to God for their treatment of the poor and needy?
In fact, Nietzsche's teachings against the necessity of religion have been some of his most long-lasting and effective. The Western legal system is still largely Judeo-Christian in that it contains laws protect each citizen against the attack of others, which Nietzsche specifically decries. But, in the West, it has become far more safe and respected to express atheistic ideas, especially in literature and philosophy.
The Importance of Logical Puritism
An important comment is made in the text, when Nietzsche accuses Kant of moralism in the section titled, "A word against Kant as a moralist." The effect of the accusation is that if you say you're not a Christian, that should have drastic consequences in your perception of the world. If, for instance, Kant still harbors feelings of morality as a system, then he has failed to allow the logic of atheism to run its course, for whatever ulterior motives he might have. For more on Nietzsche's view on intellectual integrity, read "The Parable of the Crazy Man."
The Evil of Religious Institutions
If Nietzsche is correct in asserting that the only proper view of good and evil is the purely naturalistic, then the religious and legal systems that depend on Christian morality have robbed the powerful of a great deal of wealth and stature. Not to mention that if there are laws which prevent one man from exerting his power to harm another man, then many have been punished for what is purely normal and natural and good.
The Antichrist explains how at the root of this philosophical schism is the agenda of the church and other religious institutions. Nietzsche is fearless in condemning the actions of the church, and indeed he argues that the powerful in the church are manipulators and thieves. He says that their entire policy is based on pity, which as a system seems disgusting and wrong to Nietzsche. He explains throughout the corpus of his writings that Christianity essentially amounts to sheep ruling over lions to the benefit of the other sheep.