Consider this previous answer for a related question: https://www.reddit.com/r/AskHistorians/comments/33nrg8/historically_speaking_does_it_make_sense_for/
"Rise and Fall of the Western Civilization Course" is the relevant article to read if you want an in-depth exploration of the matter. You can find it for free online, I read mine through JSTOR. Gilbert Allardyce The American Historical Review Vol. 87, No. 3 (Jun., 1982), pp. 695-725
This isn't really a new process...the usefulness of Western Civilization as a survey/general education course has been debated for a while. And I'll point out that it is being sidelined as a GENERAL ED course (as in something you would take as the foundation of a degree no matter what your major is). There are still specialized courses focusing on Western Civilization or related concepts around, they're just not compulsory anymore (and I'm sure there are still some colleges that do still have it as general ed).
The gist of Western Civilization as a course is that it tries to tie multiple different civilizations and historical events such as the Greek city-states, the Roman Republic, and lots of western European history into one long, contiguous progression of values that ended in a common bond between the USA and Western European democracies.
The creation of this course comes from the two World Wars and their aftermath which started to bring the USA into global affairs, and the ensuing post-war years saw a very enthusiastic promotion of USA/Europe as children born from the same mother ('Western Civilization'). This was an important idea to promote in liberal arts circles like universities, especially ones that also wanted to promote a sort of citizenship quality among students. It became the bedrock of what being a well-informed voter meant, hence why it would be a general ed course.
European countries sharing ideals across boundaries with the USA is a nice thought. However, questions crop up pretty quickly when one looks at policies of colonization and imperialism that also seemed to be promoted by this ideal of 'Western Civilization.' The elevation of western civilization by this course went at-odds with the slow academic work being done that would reveal the depth, exceptionality, and even commonalities found in NON-western civilizations. Traits that made the 'strict progression of values' idea seem defunct (I think it's called the Whig theory? Not sure on that). That would bring up the question about whether colleges were really educating students if they focused on just Western Civilization and ignore the intricacies of difference between European countries, ancient 'western' civilizations, and modern USA...and also treated non-western civilizations as foreign or 'backward' on that strict progression theory. This is probably not useful to promote to all students, even the students that aren't studying anything near history or government.
I feel like I'm rambling. Does this make sense? Western Civilization is slowly phased out as a general Ed in favor of World History, which usually covers the important aspects of western civilization anyway, just with more nuance and attention paid to non-western countries and history. Western Civilization basically stopped being a course promoting a good understanding of history...but it didn't go away. It's mostly migrated from survey courses to certain majors and specialties like political science, philosophy, etcetera. At least that's my experience.
I'll end this by saying I am NOT a professor, maybe someone who is can give more detail to the answer and experience.
EDIT: shoot forgot to ping previous answerer again.../u/b1uepenguin