Dahl starts with differentiating democracy against anarchism. He defines anarchism as basing on four assumptions (Dahl 1989, 39ff):

1. No one is obligated to support a bad state.
2. All states are coercive.
3. Coercion is intrinsically bad.
4. A society without a state is a feasible alternative to a society with a state.

Following from the assumptions he draws five conclusions that would explain the need for anarchism (41f):

1. Because all states are necessarily coercive, all states are necessarily bad.
2. Because all states are necessarily bad, no one has an obligation to obey or support any state.
3. Because [1 and 2 hold true], and because a society without a state is a feasible alternative, all states ought to be abolished.
4. A democratic state is still a state, still coercive, and still bad, [if it just provides procedures for inherently bad coerciveness].
5. Because the requirement of unanimity would prevent coercion, […] a democratic process would be justified if it were to require unanimity. But since a unanimity requirement would guarantee that no one could ever be coerced, an association in which [all] decisions were made by unanimity would not be a state.

He then shows why the assumptions and thus the conclusions are wrong or unsatisfactory:

On coercion (45f):

• If coercion is intrinsically bad but might be accepted for sufficiently good purposes, one might justifiably argue to create a democratic state in order to maximise other values like freedom, equality, security, and justice.
• If coercion is absolutely forbidden but likely to be employed by wrongdoers, then the argument is self-contradictory. Either one permits the wrongdoers to coerce others or one has to use coercion to stop wrongdoers from doing so.

On the need for a state (46f):

• It is empirically not plausible that humans can live together in large groups in harmony in a stateless society.
• Nearly all area of the world is covered by states, thus there is not enough space to live somewhere autonomously without a state.
• Therefore “it would be better to try to create a satisfactory state than try to exist in a society without state”.

In his critique of anarchism, Dahl also addresses Robert Paul Wolff’s defence of anarchism and shows that his arguments are self-contradictory.
In his summary, Dahl points out that there will always be coercion and the need to build a state. He believes that the “best possible state would be one that minimizes coercion and maximizes consent, within limits set by historical conditions and the pursuit of other values, including happiness, freedom, and justice” (57). In his view, this state would be a democratic state.

Dahl continues with defending democracy against what he calls “guardianship”. He defines guardianship as the idea that a small minority of persons “who are specially qualified to govern by reason of their superior knowledge and virtue” should govern the rest (52).
In Dahl’s view, guardianship rests on a couple of propositions that are difficult to justify. If a small minority of persons should be more qualified to govern due to their knowledge, this implies that a) there exists an objective, absolutely true science of governing that b) can only be acquired by some people (65f). If either a) or b) is false, the entire proposition is false.
Said knowledge to govern can either be moral knowledge or instrumental knowledge (66ff). However, most people would agree that absolute moral truth and thus an objectively true moral knowledge of government do not exists. As for instrumental knowledge, it is difficult to argue why this knowledge could only be acquired by a small minority of people.
Dahl sets as given that a good government – no matter if democratic or guardianship – acts in accordance with the public good. This leads to the following problem: Even if one assumed that there indeed exists a class of guardians with superior knowledge, these guardians would still need to find out about the public good. Dahl argues that one needs a satisfactory principle to distinguish the general good from individual interests. In his view, this principle would be democracy (74).
While for Dahl it is highly doubtful that guardians would possess superior knowledge, one might still argue that they have higher virtue. An advocate of guardianship might for example argue that guardians are no more likely to abuse their power than democratically elected officials to whom authority has been delegated. However, in guardianship, authority is alienated from the people and not delegated to the guardians. Guardians thus face an agency-conflict because they do not need to justify themselves for their action towards the people who have “lent” the authority (76).
Dahl also mentions that absolute power tends to corrupt people, but also admits that this is rather a general judgement than a valid “law” (76).
Eventually, historical experience also does not support guardianship. If one would use a “maximin” decision-making strategy to choose a political system, thus a system that is best in its worst outcome, a bad democracy leaves the people better off than a bad authoritarian regime (e.g. like the authoritarian regimes in the first half of the 20^th century). The same holds true for a maximax strategy, because in its ideal outcomes democracy and guardianship would just differ in the freedom of ordinary people to participate in making political decisions. Although both ideal systems would always make the right decisions, democracy would give people the freedom of participation, while guardianship would not. Consequently, democracy would be better (78f).

Sources:
Dahl, Robert A. (1989): Democracy and Its CriticsNew Haven and London: Yale University Press