Say you want to unpublish a piece of content that someone else originally authored. If you just go straight to the piece of content and click unpublish, you may find out that you no longer have the edit operation available to you on the content overview page. This is by design. Only the author should be able to publish a piece of content. You wouldn't want someone else publishing your content that you're still working on, would you?
To ensure you are able to edit a piece of content once unpublished, you need to set yourself as the author of the piece of content. The author is set in the "Authoring Information" dropdown.