I am not sure what you mean by moving tasks between projects and categories?
Are you referring to the Syllabus tab?
In that case, the entry in the syllabus is simply linked to a task, and you are just copying the entry not the task. It makes no sense to move the entry Midterm from English to Biology.
In your case you are probably using the syllabus task as your project view, which works fine in most cases. In future versions of the product we will make project management easier to use.