The real reason, of course...

 ...is that they want to carry out their work in an opaque bubble, safe from the scrutiny of parents and other taxpayers: "Publicly posting course syllabi will harm North Carolina’s universities".

The University is supposed to be a place where there is a free exchange of ideas, learning, and conversations that develop critical thinking. This is essential for growing a healthy workforce in North Carolina. Publicly posting course syllabi will stifle this free exchange of ideas and lead to safety concerns for campus communities.

Publicly posting required course content and course objectives can lead to the weaponization of this information. This will produce a chilling effect where faculty feel pressure to self-censor the content of their courses to avoid being pulled into the political spotlight. As a result, students will be exposed to a smaller range of viewpoints, which is antithetical to the UNC system’s own “Equality Policy.” Students need to be exposed to a range of ideas so that they can develop their own thoughts and opinions.

I guess the "free exchange of ideas, learning and conversations" is supposed to be a closed system, is that it? The tax-paying part of society shouldn't have any say so in what constitutes a quality education? And I have to laugh when contemporary professors talk of their fear that "students will be exposed to a smaller range of viewpoints". Somehow, I do not think they are worried about the extinction of conservative viewpoints, which are becoming impossible to hear on many college campuses because of the the threat of violence by "progressives"; more likely, it is the burgeoning fields of toxic, left-wing fantasy that they seek to protect, to insulate from oversight, their mission too often being to indoctrinate, rather than educate. 

Always beware of people, especially in an academic environment, who argue against transparency.