According to Weber, disenchantment and rationalization are irreversible because they develop through a historical process that itself has no "outside" or rational end governing it. Again, the reason that the iron cage is iron is because the institutions and rules governing the interactions of agents are themselves rational, the products of reason. They're geared, ideally, toward efficiency. This means that there's no rational purchase point one could get outside of the iron cage from which one could critique it. The only rational critique one could form of modern society that would carry any normative weight would be the complaint that it's not rational enough. But as for the whole of disenchantment and rationality, there is no reason or rationality that may judge or qualify it, because rationalized reason is our reason.
Weber's complaint about rationalization is that it fails to acknowledge its own "religious" or vocational presuppositions. For example, we can devise more efficient and successful ways to extend life, but we cannot explain, on the basis of natural science, why a human life is worth preserving let alone extending. If disenchanting reason provides a total account of how the world, in fact, is, and if this account turns a blind eye toward values, then modern life becomes, essentially, meaningless.
Nietzsche similarly complains that modern rationalism is still theological. According to Nietzsche, all of the institutions of modernity -- modern science, with its reliance on causal, deterministic accounts of the world, liberal-democratic politics, romanticism, humanism, "free thinking," pragmatism, socialism, etc. -- are essentially Christian or express the psychological and moral interests of Christianity. Asceticism, self-denial, ressentiment, weakness, and a slave mentality are all phenomena we ought to understand as consequences and implications of the most basic "drive" of all Western institutions: the will to truth. Again, modernity is supposed to be a rationally defensible, self-grounding, and hence independent, fully secular form of life. Yet, according to Nietzsche, all the modern claims for independence ironically express a deep fear of genuine independence; they're a disguised and self-deceptive form of dependence and the slave mentality. Therefore, what modernity takes to be success is in reality failure.
Adorno inflects the Weberian and Nietzschean accounts. If religious rationalism turns into self-stultifying scientific rationalism, then we must project scientific rationalism back into the historical process from which it emerged, so we may see religious, mythic forms of life as already predicated upon the instrumental rationality and identity thinking they will eventually produce in pure form. If we can come to understand religious rationalism as already instrumentally rational (as "enlightening," or as a form of identity thinking), then the "religious" and the "secular" are co-extensive. Religion contains a rational kernel, but scientific rationality contains a mythic core (i.e., there's something inherently irrational about treating the world as though it were causally explainable through and through). And contrary to Weber and Nietzsche, the solution isn't simply exposing the religious presuppositions of secular thought; rather, it is exposing the problematic conception of rationality they both share: identity thinking.
Disenchanted reason and mythology are both forms of identity thinking: subsumption of sensuous particulars under explanatory, coherent, unifying universals, whether those universals be myths, gods, natural laws, or concepts. Rationalization is the increasing comprehension of individuals by means of their participation in conceptual schemes whose elements are invariant and unchanging. Where the grammatical structure of moral insight entails the performative realization of the good, the grammatical structure of rationalization is one of subsumption.