NOTE: Could somebody in the know possibly give me an estimate of the cost of building with wood versus metal? It would be a nice detail to include.
The future is a pretty awesome place (purportedly; we seem to be having some difficulty getting there in a reasonable period of time, so we'll have to wait and see). Robotic maids, Humongous Mecha
, hardwood flooring...
...Okay, maybe not that last one.
In a futuristic setting, objects and buildings constructed of wood tend to be a pretty rare sight, with metal and/or plastic being far more common. This usually goes hand-in-hand with an aversion to other "primitive" building materials, such as brick or stone.
The most likely reason for this is that wood and similar materials just don't look futuristic enough. Much like how Our Weapons Will Be Boxy in the Future
and how Everything Is An iPod In The Future
, metallic architecture serves as an elegant visual cue for how far removed (temporally speaking) the world in the story is from ours. Removing this cue can disorient the viewer ("Wait, this show is set in 22XX? Since when!?"), so a bit of mild implausibility that doesn't matter much in the long run and which nobody will really notice or care about
is a good trade-off.
Also, there are many situations where this is justified. There are places where wood just isn't practical or isn't worth the trouble of importing; more cynically, sometimes there are no trees left, period. This trope comes into play when "primitive" building materials are avoided outright, with no easy-to-find explanation.