Because the Assignments module contains important work, the teacher is given less control over deleting messages than he has in other Manhattan modules. Manhattan's developers have learned through experience that despite pop-up warnings and other "Are you sure?" prompts, when given the ability to delete assignments, even experienced teachers have accidentally deleted important assignments containing say, the final papers of 20 or 30 students in the class.
Another reason for limiting the messages the teacher can delete within the Assignments module is that it keeps everyone completely honest. Suppose a student claims that they submitted their final paper for a course via the Assignments module. If you had the ability to delete student submissions, the student could make the claim "I sent it, but you must have deleted it!". Since you can't delete a student submission, even if you wanted to, such "accidental" deletions are impossible. Once a student submits work for an assignment, that submission is "set in stone". The date and time as well as the contents of the submission and when the teacher first opened it is a matter of fact.
Therefore teachers can only delete:
Assignments before any student has posted a reply.
Any message, other than the actual assignment, sent by the teacher back to a student.
The second item above means that you can delete a message that you've accidentally returned to the wrong student. Simply open the message, and use the checkbox and Delete button at the bottom of the message to permanently delete any message you sent to a student in error.
Of course, accidents will happen. Suppose you post a new assignment that is full of errors, or that you didn't mean to post. If a student replies to the assignment (usually with a message that asks, in effect, "Huh?") you can't delete the assignment. You can, however, click on "Manage Topics" within the Assignments module and manually "hide" the message from your students, and keep it hidden for the remainder of the course. See Teacher hidden and scheduled topics for more information.