I assume you are trying to delete a Subject that you created. Check the Subject by opening it to ensure it does not have a Parent Subject or is not a Child of another Subject. Although this should not restrict you from deleting it, it doesn't hurt to check.
As long as you have rights to delete a Subject then you should be able to delete it from the Subject console in Business Management. Are you in that Console? If not, you might be trying to delete a different type of record or possibly the Subject has been applied to a record in CRM that is closed like a Case, Service Activity or some other type of record.