Cannot cook in furnace; unable to place wood or burnable items

I thought that I would be able to cook something in the furnace. When I clicked on the furnace, the item I wanted to cook got in the furnace fine, but I could not click the space that allowed me to put the item I wanted to burn.

I was unable to cook anything
and I could not get it out of the furnace.
Nor was I able to get a burnable item in the furnace.