If you teach composition, you will train students in grammar, and there is a finality to that grammar.
If you are a linguist, what you teach and learn about grammar its that It changes, varies, and is generative. Grammar is open.
I'm familiar with both. I tried to explain to a linguist why teaching grammar was important to teaching writing, and the linguist couldn't understand my points. Because grammar As open knowledge is nothing like grammar as closed knowledge.
Even a good pop star works in a tradition to which they are responding and in which they are educated. That education in that case won't take place in a university. But out is an example of what is meant by education and culture.
Universities help maintain a different kinds of culture. Increasingly a global culture, which involves a classical tradition. This includes the arts and literature, the sciences and social sciences, philosophy and theology. One must be educated to contribute to these things, to the creation of knowledge and understanding in them.