Define your terms.
The division of labour is the distribution, be it spontaneous or centrally imposed (within the state or within the household), of different tasks to different people. "Division of labour" is simply a technical term in economics to describe the phenomenon of cooperation. Some people are better at defending the community, some people are better at agriculture, some people are better at crafts. Technologically advanced societies need to be complexly organized, thus creating a class of bureaucrats, managers, and entrepreneurs, but division of labour occurs in every society. In fact, it is the definition of "society."
As Ludwig von Mises points out in Human Action, there are three specific conditions that makes this arrangement desirable (157):
1: Different people have different abilities.
2: Different areas have different resources.
3: Some jobs require an effort beyond the capacity of a single person.
Because the first two conditions hold almost universally with respect to almost any endeavour, and because the third condition holds for most of those tasks which are required to maintain and advance our standard of living, we can expect the division of labour to be almost universal to human behaviour. And, in fact, it is: Every society, from "late capitalism" America to the simplest Eskimo band, has a division of labour of some sort. In simple societies, where economic tasks fall into broadly different types, the division occurs along lines of age, lineage or, above all, gender – this latter division being particularly convenient for a species with gender dimorphism as pronounced as humanity's.
It is tempting to say that a wealthier society demands a much more complicated division of labour, but this is getting the causal chain backwards. A more complex division of labour permits a much higher standard of living. At a certain point – very early on – a society will find itself with the potential to move beyond the point where any one person or central authority can organize it methodically. Historically, civilizations which reached this point have responded in only one way: by trying to organize it centrally anyway.
The results have invariably been civilizations that were frozen, unable to advance. The longest-lived civilizations, like ancient Egypt and classical China, remained at the same technological level for hundreds of years without significant technological or social change. They're the lucky ones; the unlucky ones fell rather quickly – getting conquered, unable to reorganize for war against a more fluidly organized opponent (Egypt, Rome, Aztec) or simply fading into mediocrity because their new policies make it impossible for subject/citizens to compete with foreign business (China, Britain). These societies did not do away with division of labour – they flash-froze it. This imposition made it a liability rather than a strength.
The whole point of capitalism is to make the division of labour a spontaneous response to the predicted rewards of the general public rather than the fiat of any oligarchy or ochlocracy, regardless of whether they claim to act in the interests of said public. This is effected via the market. In a free market, entrepreneurs, speculating as to the desires of consumers, offers the fruits of their labour; consumers offer credit in the form of money. A price is negotiated, and the entrepreneur uses the credit acquired to secure their own desires which, because of the time it took for their enterprise and because of their own natural deficiencies, they could not through their own labour. That's the theory, anyway.
In the case of managers, the service they offer is the organization and administration of a highly complex enterprise involving multiple tasks and therefore multiple workers. There are many ways they can go about doing this, depending on the task at hand, the people involved in the project, and their own abilities and preferences. In the Western tradition, the received way of doing this has been hierarchical management.
Hierarchical management is a management strategy in which an enterprise is split into the most economically convenient tasks, with workers being assigned roles according to the predictions of a central executive. Hierarchical management was the modus operandi of the Industrial Revolution; in the early 20th Century it was considered to have been perfected by Frederick Taylor.
As Michel Foucault points out in Discipline & Punish, hierarchical management was not invented by capitalists; it was invented by monks. During the "Classical" era of our civilization – ie., the "Enlightenment" – this particular technique for the division of labour came to be applied to almost every sector of life: the workhouse, the army, the orphanage, and above all the prison.
But surprise surprise: What was a great technique for the craft manufacture of diligent ascetics turned out to be mind-numbingly boring and demeaning for workers, and dehumanizing for orphans and prisoners. The constant examinations, the condescending managers who can't be bothered to reward initiative but who are all too eager to punish the slightest deviation from the prescribed regimen – these hallmarks of modern industry have caused so much suffering that the whole conceptual system with which they are associated, rightly or wrongly, has come under attack.
Capitalism is the name of the system which uses the free market as a tool for organizing a division of labour in a new, less wasteful, more peaceful manner than any other historical model. Hierarchical management, as it has been implemented in our civilization, is a grim tool for social control, a playground for petty people to trip out on power. It is one form of the division of labour, which is a precondition for the existence of society, but it is neither the best example, nor the only historical example. Other divisions of labour are possible within a free market. Confusing them is equally disasterous for supporters and critics alike, and attacking the "division of labour" on the basis of the flaws of hierarchical management is throwing the baby out with the bathwater.