You still have to select the book to sync in iTunes. I assume that you downloaded this book on your computer. The left sidebar of iTunes is somewhat irrelevant as to what is on and not on the iPad. You are seeing what is in your iTunes library - that's all.
Connect the iPad to the computer and launch iTunes.
Click on the iPad name on the left side under devices.
Click on the Books Tab on the right.
Make sure that the book is selected to sync. Check the box next to it if it isn't.
Click on the Sync Books Heading.
Click on Apply in the lower right corner of iTunes
BTW... Double clicking on a book in the iTumes window will not open the book. You can double click on a PDF in the iTunes window and open those files - but not e-books.