I cant understand what makes carbon fiber stiff.What kind of magic happens between carbon fibers and cured resin that makes the resulting material so stiff?

To be more specific,I mean stiffness in the perpedicular direction to the surface.

Carbon fibers alone are stiff,but only when the force is perfectly parallel to the direction of the fibre and the fibre itself must be stretched.Except the stretching scenario,it have practically zero stiffness,its really just a wire.

If we imagine a sphere made of CF,how would it be any stiffer than just resin when the applied force is perpendicular to its surface? Like if the sphere had vacuum inside so the outside pressure would try to compress/squeeze/flatten it.

I cant think of anything that would make it any stiffer in such scenario than the resin matrix alone.Carbon fiber ball alone without resin is about as stiff as socks,the resin is stiffer and will hold its shape but its still just polymer,its stiffness is low.

Why when we combine woven fiber ball with zero stiffness with little bit of resin with low stiffness,we get high stiffness? I asked this before and the answer was that the resin holds the fibers,but that doesnt make any sense to me.The resin is weak and low stiffness,if it holds the fibers,that have zero stiffness perpendiculary to the surface,the force will just be transfered to the weak and soft resin and as result it cant be any stiffer than just the resin alone.