Tom, the problem is not flexural stiffness but more so torsional stiffness. Depending on the fibre orientation of the layup, a carbon rod may not be very stiff in a torsional/ twisting sense. Some carbon rods have a primarily longitudinal fibre orientation and they are not stiff in a torsional sense. Others have a helical layup and they are reasonably stiff in a torsional sense. I discovered this issue on my Carf mig 29 where I was dealing with rather large stabs that magnify the problem.
i think Vince is suggesting a lack of torsional stiffness.