The bug
When you click with flint and steel at blocks where no fire can be placed because the position is occupied by another block, the flint and steel item is still damaged and acts like it was successfully used, preventing an off-hand item from being used.
How to reproduce
Place a fence on top of a full block
Try right clicking with the flint and steel item at the top of the full block
→ The item is damaged but no fire block was placed
The reason
The following is based on a decompiled version of Minecraft 1.10 using MCP 9.30.
The reason for this is that the method net.minecraft.item.ItemFlintAndSteel.onItemUse(ItemStack, EntityPlayer, World, BlockPos, EnumHand, EnumFacing, float, float, float)
always damages the item even if no fire block was placed.
Linked issues
relates to 2
Comments 4

What you are talking about is probably MC-4923. This one here happens also when no fire is placed at all.
Also present in 16w33a
Can confirm for MC 1.12.1.
This is because the flint and steel places fire, but afterwards, the fire decides if it can be there after the flint and steel becomes damaged.