By definition, anarchists oppose merely government, not order or society. “Liberty is the Mother, not the Daughter of Order” wrote Proudhon, and most anarchists would be inclined to agree. Normally, anarchists demand abolition of the state because they think that they have something better to offer, not out of a desire for rebellion as such. Or as Kropotkin put it, “No destruction of the existing order is possible, if at the time of the overthrow, or of the struggle leading to the overthrow, the idea of what is to take the place of what is to be destroyed is not always present in the mind. Even the theoretical criticism of the existing conditions is impossible, unless the critic has in mind a more or less distinct picture of what he would have in place of the existing state. Consciously or unconsciously, the ideal, the conception of something better is forming in the mind of everyone who criticises social institutions.”

There is an anti-intellectual strain in anarchism which favours chaos and destruction as an end-in-itself. While possibly a majority among people who have called themselves anarchists, this is not a prominent strand of thought among those who have actually spent time thinking and writing about anarchist theory.