Is it wrong to deny access to professors when they request to join a STUDENT Facebook group?

[chicagonative13]

The group is not abusive about professors, but occasionally a student will discuss frustrations and problems with certain professors, in a professional manner (as in, not "omg he's such a horrible teacher", but rather "he gave us way too much homework, I don't know how I'm going to finish it all"). The issue is, a student posted that they were frustrated with a certain professor. Another student took it upon themselves to alert the professor in question, and now said professor is requesting to join the group. I am the creator of the group, and therefore the administrator. The group is closed, so the professor cannot see the posts. The description of the group says that it is for students. Is this enough reason to deny the request?