Historically, critical theory arose between the wars in Germany. Many of the early critical theory theorists were Jewish, and they saw Germany between the wars become obsessed with its lost birthright. A great deal of work was done on the idea of a "pure" German character, something mystical and known only to true Germans.
This suggested a metaphysical position that critical theorists were very uncomfortable with. It suggested a shared delusion, not one based in real social conditions but in fables. Fascism became the first great target of Frankfurt School theorists.
What's fascism? See here.
You might get the idea that since one of the major theorists for critical theory is Marx, that the USSR might be some sort of ideal society for them. You would be wrong. Communism, especially in its Eastern European versions, was recognized as brutal, overbearing, and alienating. In fact, critical theorists are sometimes known as followers of "Western Marxism", which manifest itself as social and linguistic critique, rather than "Eastern Marxism", which manifest itself as political change at a state level.
What's wrong with Fascism and Communism, according to critical theory? Most of us would think the problems are obvious - lack of freedom, presence of coercion. It is worth noting that both believe they are appealing to a higher sense of freedom. Fascism thinks that there is something metaphysical, which the state needs to nourish and support. If that can be found, people will be truly free. And communism thinks that people get fooled by the illusion of freedom; they don't have the real thing under a capitalism system. They need to have true freedom, rather than illusory freedom.
The nature of freedom is certainly worth discussing. However, what became increasingly clear was that freedom was not possible in either of those societies. Quite the opposite - the worst forms of oppression and brutality happened under fascism and communism.
Many critical theorists fled Germany when the war came (remember, many were Jewish). Some came to the US. Some stayed after the war (e.g., Herbert Marcuse). And the lessons that were learned in opposing the obvious evils inherent in fascism and communism were applied to technocratic, corporate American culture.