Some of them are 20. Some are 18. Some are younger. Some are older. Even if 20, there is a power imbalance, especially in a university situation. It is the possibility of such a power imbalance (leading to a conflict of interest) is what makes it unprofessional, not her age or ability to make rational decisions.

Older article on the subject:
http://www.nytimes.com/1993/05/09/nyregion/student-faculty-dating-it-s-not-in-the-rule-book.html