If the book is in Archive, you won't be able to delete it from Kindle for PC. You can only permanently delete a book from your Archive by going to the Manage Your Kindle page. Be aware you would have to repurchase it to read it again, though.
If you are looking at "All items", it shows both downloaded and Archived items. I always pick either downloaded or Archived items, so I can keep track of which books are actually downloaded to my pc.