Why are people using with carbon and Kevlar woven together?
Carbon is very stiff and Kevlar is like nylon (anchor rode) with lots of stretch.
What am I missing?
Your presumption is wrong. Kevlar is NOT like Nylon. I have no idea where that notion came from. Kevlar is actually quite stiff--that is, it has a high modulus of elasticity, roughly between S-glass and Carbon fiber. Kevlar is also quite strong, particularly in tension, again between S-glass and carbon fiber. Where Kevlar falls down is in its compression strength--it is very low. It is below the compression strength of S-glass and even E-glass (E-glass is the common boatbuilding fiberglass, and S-glass is a higher grade of fiberglass that is sometimes used, particularly in military applications. In fact, S-glass is the military-grade version, and any non-military grade is called S-2 glass.)
Kevlar was once used for sailboat standing rigging because of its strength and stiffness. But as carbon fiber technology developed, it surpassed Kevlar as a rigging material. Kevlar is also highly susceptible to ultraviolet light degradation. Carbon fiber also replaced Kevlar in the making of sailboat sails for these very same reasons.
So, why mix carbon fiber and kevlar in woven weaves? The reason is to get the toughness of Kevlar into a laminate without sacrificing strength, at least by too much, anyway. As we all know from bullet-proof vests, Kevlar is, literally, bullet-proof. So some mixes of carbon fiber and Kevlar may be a good combination if you want a high-strength and stiff hull that is bullet-proof. Where Kevlar falls down in compression strength, carbon fiber can take up the slack. The overall laminate will not be as stiff as an all-carbon laminate, but it will be more impenetrable.
Personally, I have never really liked Kevlar in boat hulls because of its low compression strength. If you were going to use a hybrid material, a mix of carbon fiber and S-glass would make a lot more sense--there are positives all around with such a mix. In boat structures, there are plenty of areas in hull panels and structural joints were compression forces are very high, and you don't want Kevlar in those areas. Also, Kevlar is a devil to repair. If it is too close to the hull surface where it can experience abrasion, good luck in trying to make a fair repair. Kevlar is extremely hard to cut (you need special cutting shears) and once abraded, it is nearly impossible to get the abraded edges sanded down and laminated over. Most people who try to incorporate Kevlar into a laminate usually get its location and placement wrong so that it does not work effectively.
I hope that clears things up a bit.
Eric