SpaceX is spending considerable effort to catch Falcon 9 fairings into a giant net on a ship. I am aware that salt water ruins almost everything in the long run, but the fairings are a composite material and seem to be painted. There are carbon fiber (and fiberglass) boats, so why can't Falcon 9 fairings just touch the water (even for brief time)?
The fairings are not boats. While they appear to float (at least for some time), there will also be water on the inside of the fairing. That results in some issues. Inside the fairing, there are electronics and other corrodable materials. Now the fairing is designed to be as light as possible. Therefore, SpaceX probably doesn't want to make the entire interior waterproof and corrosion resistant. This results in electronics getting wet, corroding and therefore possibly being damaged.
Imagine if you drop your phone in the water for a short period of time: although it is still alive, you have to take it apart and dry it thoroughly. SpaceX has the same issue but with an added twist: everything can start to corrode while it's wet. They would most likely have to take the entire fairing apart, dry it, re-assemble it and test for functionality. Even then, if the corrosion has started (but is still within acceptable parameters), the fairings' lifetime is reduced.
Besides the inner workings of the fairing, there is also an aluminum honeycomb structure between the composite layers of the fairing. If salt water were to enter this layer, further damage could occur. Therefore, although the fairing is marketed as a composite structure, it is not purely made out of carbon products. (Thx @Hobbes)
In conclusion, the main point is that although the main structure of the fairing consists of composite materials, the inner parts do not.
In addition to the water damage is the impact damage: the fairings wouldn't "touch" the water they'd hit the water, even with parachute retardation. A net slows deceleration down and spreads it more evenly across the structure, which is a lot friendlier to the materials and the supporting electronics.
One of the biggest concerns in spacecraft is keeping them free of contaminants. Spacecraft are often built in clean rooms to keep them free of any such thing. Landing in salt water would leave residue on the fairing that would be virtually impossible to clean. Outgassing from any residue could lead to damage to the payload. Source.
Even with a parachute there could still be structural damage if it landed in the ocean. The impact might not be great, but how can they know for sure. Also the waves impacting the fairing could cause structural stress.
Looking at pictures of the half-fairing taken from the recovery ship, it doesn’t look worse for wear, and it doesn’t appear to have been damaged when it hit the water. Assuming it’s okay (a big unknown—it may very well have irrevocable structural damage), it’ll be the first time in history that a rocket fairing has been successfully recovered.
Clearly it might survive the landing. But it's not worth risking a future mission on a structurally stressed fairing.