Carbon bikes make me nervous. Can you ease the tension?
Carbon fiber is stronger, and far less susceptible to fatigue than any other frame material on the market. It can be engineered to have the strength of titanium, the ride quality of steel, and the stiff and powerful performance of aluminum at the same time. 

I have only broken 2 frames in my life. Both were aluminum, ridden far beyond the fatigue life of the metal. I have seen carbon break, but usually it is in a major accident. A car crash or something similar. 

If a carbon frame cracks from fatigue, it shows small crack in the paint, then splintering, and then it will look like crushed bamboo when it fails fully. The frame will last longer, and you will have more warning of failure on carbon than any other material. 

As for why you should choose it, it makes your ride more comfortable, more stable, and more pleasant. It's also lighter, but that is at best a secondary reason.