Carbon fiber isn't going to replace wood body guitars anytime soon, but for those who want something different there are some definite advantages to using carbon fiber. As I understand them, the main reasons to use carbon fiber over wood construction (besides looks) are acoustics, durability, and ease of construction.
I don't know a lot about the science behind guitar construction, but I'll point you to Blackbird Guitars
and Rainsong Guitars
, two carbon fiber guitar makers that do a good job explaining the logic of using carbon. But my understanding is that properly constructed carbon fiber guitars have a very clear sound and loud volume. More importantly, once one finds a good design for a carbon fiber guitar, it's much easier to repeat success than with a wood guitar. Every wooden component can vary slightly - grain direction, moisture content, knots or defects, etc... - there is a lot less variation between sheets of carbon. So it's easier to crank out duplicate models with reliable sound qualities.
In addition to the stability of the materials, carbon fiber is just plain durable and strong. Carbon fiber (and other composites) are not affected by weather and humidity the same way that wood is. Improper storage of wood guitars can seriously damage the joints between components, whereas carbon fiber wouldn't bat an eye traveling from the dry desert to the tropics in an instant. Carbon fiber is also just plain strong - before I installed the wood components, I could easily lean my whole body weight into the guitar shell. I didn't test it, but I might have been able to stand on it without a crack.
Since my guitar is a mixed carbon fiber - wood construction, I don't get all of these benefits, but it's still darn strong. I don't worry about hurting the body, and if any part of the guitar gets damaged down the road, I feel it would be a lot simpler to patch it up or even re-build the entire top than with a traditional wood guitar.
Ease of construction
The second half of this project, installing the wood components and strings, was exactly like making a traditional guitar. But compared to a traditional guitar, making the body was dead-simple. I think the skills involved are more accessible for beginners compared to wood construction. In just one night I went from a bottle of epoxy and a pile of fabric to a nice guitar shaped body ready for finishing.
That same ease of construction made customization a lot easier. Instead of buying or making multiple special guitar jigs, clamps and tools, one need only change the mold to whatever shape is desired. I chose to make the standard design given to us by the instructors, but others in the workshop chose to customize theirs a lot - from making cutouts and sound-ports in the side, to making a bass guitar.
That customization does come at a price, of course. While spruce and other standard guitar woods can be pretty cheap, carbon fiber is definitely not cheap. And while the laser-cut mold came cheap to me as a member of Techshop, I don't know what the same service would cost from a third party. But these costs might be reduced with some creativity - making a non-laser cut mold out of foam should be possible, and perhaps other composites besides carbon fiber could work as well.