The beginning thesis is that all governments exist solely for the purpose of the powerful to exploit the weak. The rhetoric is Marxist and the Bourgeoisie are assigned as the primary source of evil, with religion being merely something that was designed by the powerful to oppress the poor. I think it is safe to say that Malatesta is an atheist. He asserts that no matter how altruistic a government might appear, it is primarily a vehicle for oppression.
In the middle of the book, he describes a supernatural revelation that he received from Darwin: That all animals (e.g. ants) have natural organizational structures provided by evolution. Taking away government would thus allow this biological determined organization to reassert itself. We will set aside the fact that survival of the fittest gives a natural advantage to the worst sorts of human character.
So what is this natural system? Errico gives it the name "solidarity". This is a system of mutual support based on altruism and caring as much about others as you do about yourself, which he asserts is the natural evolutionary state of mankind. Summing it up, he says, "This society of free friends would be anarchy".
The objection was raised that someone must deal with the post office, law and order, and military affairs. In our day we know that the government isn't needed for a post office, but what of the others? Errico observes that where there are no police, there is no crime, while most of the crime happens in areas where most of the police are. Thus, he deduces that police are the cause of crime because they provoke people to criminal behavior! Similarly, armies provoke war.
I should admit that I am sympathetic to some of the ideas. Collective action by interested individuals joining together for a purpose without undo governmental regulation is a core American principle. Still, that is a long ways from the pure libertarianism that Errico is advocating. He wants to abolish private property, which has been tried in the decades after his death and failed miserably. The missing ingredient in all this is "Evil", which is a concept that atheists simply can't come to terms with. Humans are by nature Evil, even though they might do something good now and then. Errico ignores this problem by attributing evil to the Bourgeoisie only.
The book ends with a "We shall overcome" prophecy that deserves a smirk as America and Europe experiment with Total Government concepts. His work finishes with a gem that is certainly appropriate for today:
"How solve this problem of social alchemy: To elect a government of geniuses by the votes of a mass of fools?"