Why do simple optical fibers usually support only half-duplex communication?
Why can't simple optical communication systems transmit and receive light of a single wavelength in parallel?

Because it's difficult to isolate the receiver from the transmitter, and the transmitter on the near side will overwhelm the receiver, so it won't be able to see the transmitted light from the far side.

Why doesn't the same problem occur when using multiple wavelengths (e.g. in Wavelength-division multiplexing)?

Because you can easily filter out the transmitted light while allowing the received light, using a wavelength-selective (i.e. colored) filter.

How does Direction-division multiplexing solve that problem?

Someone has invented a duplexer that only lets light through if it's passing in one direction, and not the other.  This is probably the optical analog of a SWR coupler for microwaves -- but I'm guessing.
They did a good enough job of it that the transmitted light doesn't overwhelm the receiver, and there you go.
I would not be at all surprised if, when you dig into it, you'll find in the small print that the range is limited, because the duplexer lets some outgoing light back into the receiver, and so the light received from the far end has to be stronger than otherwise.  But -- I could be wrong; I'm just cynical.