In general, anyone can challenge a book in libraries or schools. However, all book challengers must adhere to the guidelines and policies that have been set in place by the library or school. Examine the language of your library's reconsideration policy to determine if there are any restrictions on who can challenge.
Students may challenge a book if they feel a particular book contains inappropriate subject matter.
Family members or caretakers may challenge if they feel that the book contains sensitive material or content that is inappropriate for their children.
Community members may challenge a book if they believe it is not appropriate for the community or if they find it offensive or objectionable.
Board members may challenge a book if they believe it violates community standards or if it conflicts with the school or library's mission statement.
Politicians may challenge a book if they believe it violates the law or if they feel it conflicts with their political beliefs.
You yourself may challenge a book for any of the aforementioned reasons. As a library professional (current or future), you are still a member of the community.