This is intended behavior for unmodified Minecraft.
In previous versions of Minecraft, you could break a block with the corresponding tool in adventure mode. However, in 1.8, this was changed. Now, you cannot break any blocks by default. To allow a tool to break a block, add the CanDestroy NBT tag to it. Placing blocks is similar; it requires the CanPlaceOn NBT tag on the block you want to place.
See here for the full details.