There was a Marxist, in Italy, in 1923 who was upset that socialism was so slow to spread. He decided that the problem was that Marx only targeted history, politics and economics. That it was all of the rest of the traditional belief systems that were indirectly linked in with Capitalism and stopping any attempts to get socialism voted in. He, and a group of other academics saw that the culture was a large number of different belief systems loosely knit together and decided that these things had to go to make room for socialism to be accepted.
They started to go after religion, Christianity in particular, traditional sexual mores, nearly all things traditional,, and pushed to gain a greater separation between generations. This group joined together at the University of Frankfurt, in Germany and formed what ended up being called the Frankfurt School of Critical Theory. The rise of Nazism caused them to leave for Geneva in around 1934, then by 1935 they moved into Columbia Unversity in New York. They were stilled referred to as the Frankfurt School. And Critical theory has since spawned concepts of diversity, ethnic studies, Women's Studies, and political correctness. It is applied in sociology, psychology, history, political science, philosophy, journalism, art, etc. and it has spread over the last 80 years or so to most colleges.
I don't refer to it as "Critical Theory" but as "Cultural Marxism" but it isn't taught like that at all. It is taught as if the particular concepts (e.g., diversity or social justice, were self-evident values and they are woven into whatever the class is). The idea is to kill all things in the existing culture to make for a more fluid, perhaps chaotic, culture that will be enthusiastically supported by newer generations - those who, unsuprisingly, are more open to Marxist ideas like social justice, redistribution, centralized control of all things, collectivism and identity politics.