Another way to think of critical theory is as an alternative to existing modes of social science that were current in the 1940's and 50's. To some extent, this amounts to a critique of positivism (see later on that). But the issue in social science is somewhat different. How can we obtain reliable knowledge about the social world? What counts as reliable knowledge, and what is just folk knowledge?
Social science had, for a long time, modelled itself on the natural sciences. That meant looking for laws, or approximations of laws, that could be used to develop theories. While there continued to be enthusiasm for this approach in the middle of the 20th century (e.g., functionalism in anthropology, neo-classical economics, behaviourism, etc.), the critical theorists also realized that there were serious problems with this approach. Some of it went back to Dilthey's distinction between Naturwissenschaften (natural sciences) and Geisteswissenshaften (human sciences), which he said required two different ways of proceeding. It became clear, though, that the search for laws, and the attempt to build theories based on those laws, risked leaving out much of what was central to being human.
If we were to take freedom seriously as a human characteristic, we would need a way of thinking about how people were not free, and how that happened not only through the circumstances of politics, but also through social science itself. In other words, the very attempt to know people using a model of science based in the natural sciences, risked making them less free. If we started to put people into social-scientific categories (e.g., pathologized them or stereotyped them), we would end up limiting peoples' options. Our analysis would be a self-fulfilling prophecy, not an actual examination of the world.
So, knowing about race or gender (for instance) in the wrong way solidified problematic views about race and gender into the world. Critical theory, then, had to be a way of doing social science that both constructed knowledge about the social world, and at the same time avoided the limitations of positivistic social science.