Engels, let us not forget, argues, in effect, any activities which "replace isolated action by combined action of individuals" means "the imposition of the will of another upon ours" and so "the will of the single individual will have to subordinate itself, which means that questions are settled in an authoritarian manner." This, for Engels, means that "authority" has not "disappeared" under anarchism but rather it has only "changed its form." [Op. Cit., pp. 730-1]
However, to say that authority just changes its form misses the qualitative differences between authoritarian and libertarian organisation. Precisely the differences which Bakunin and other anarchists tried to stress by calling themselves anti-authoritarians and being against the "principle of authority." By arguing that all forms of association are necessarily "authoritarian," Engels is impoverishing the liberatory potential of socialism. He ensures that the key question of liberty within our associations is hidden behind a mass of sophistry.
As an example, look at the difference between marriage and free love. Both forms necessitate two individuals living together, sharing the same home, organising their lives together. The same situation and the same commitments. But do both imply the same social relationships? Are they both "authoritarian"?
Traditionally, the marriage vow is based on the wife promising to obey the husband. Her role is simply that of obedience (in theory, at least). As Carole Pateman argues, "[u]ntil late into the nineteenth century the legal and civil position of a wife resembled that of a slave" and, in theory, "became the property of her husband and stood to him as a slave/servant to a master." [The Sexual Contract, p. 119 and pp. 130-1] As such, an obvious social relationship exists — an authoritarian one in which the man has power over the woman. We have a relationship based on domination and subordination.
In free love, the couple are equals. They decide their own affairs, together. The decisions they reach are agreed between them and no domination takes place (unless you think making an agreement equals domination or subordination). They both agree to the decisions they reach, based on mutual respect and give and take. Subordination to individuals does not meaningfully exist (at best, it could be argued that both parties are "dominated" by their decisions, hardly a meaningful use of the word). Instead of subordination, there is free agreement.
Both types of organisation apply to the same activities — a couple living together. Has "authority" just changed its form as Engels argued? Of course not. There is a substantial difference between the two. The former is authoritarian. One part of the organisation dictates to the other. The latter is libertarian as neither dominates (or they, as a couple, "dominate" each other as individuals — surely an abuse of the language, we hope you agree!). Each part of the organisation agrees to the decision. Do all these differences just mean that we have changed name of "authority" or has authority been abolished and liberty created? This was the aim of Bakunin's terminology, namely to draw attention to the qualitative change that has occurred in the social relationships generated by the association of individuals when organised in an anarchist way.
As such, Engels is confusing two radically different means of decision making by arguing both involve subordination and authority. The difference is clear: the former involves the domination of an individual over another while the second involves the "subordination" of individuals to the decisions and agreements they make. The first is authority, the second is liberty.
Therefore, the example of free love indicates that, for anarchists, Engels arguments are simply pedantic sophistry. It goes without saying that organisation involves co-operation and that, by necessity, means that individuals come to agreements between themselves to work together. The question is how do they do that, not whether they do so or not. As such, Engels' arguments confuse agreement with hierarchy, co-operation with coercion. Simply put, the way people conduct joint activity determines whether an organisation is libertarian or authoritarian. That was why anarchists called themselves anti-authoritarians, to draw attention to the different ways of organising collective work.