When you have an item to put in the furnace, it does not show up in the menu, no matter what it is. This is only for the top spot of the menu, as it let me put wood and coal in the bottom half.
Steps to reproduce:
1. Get a smeltable item in your inventory.
2. Place a furnace and open the menu.
3. Notice, you can't put anything in the top slot.
Edit: this is a multiplayer bug, but it happens to both the host and the 2nd player. My friend was in a world with me and could not smelt anything, and nor could I, but once I left, he could. Also, make sure the 2nd player is in the game before the him/herself or the host opens the furnace, or the bug is not there.
I also have the same problem in 0.12.3. However this seems to occur in the Windows 10 version of Minecraft only.