Hi April,
I can confirm that you are not overlooking an option to allow students to delete their own posts. It is not possible (I guess) because of the nature of forum discussions, where participants post replies to other posts. If a teacher decides to delete a particular post, then any replies to the post are also deleted. We wouldn't want a student deleting their own post and the all replies to it suddenly disappearing!
Thus, I'd encourage you to consider using a different activity, perhaps a glossary or a database, where students may be allowed to delete their own entry at any time.