Glass fibre + resin is an insulator, and if lightning hits it will break down the insulation, turn it into a partial conductor, and fry the material.
Carbon fibre is a relatively poor conductor, and if lightning hits then the current flow will raise the temperature of the stuff and fry it.
Metal is a good conductor.
AIUI.
That's why composite IFR planes have metal mesh embedded within the insulated sections, to conduct the current away so it cannot ionise (and destroy) the nonconductive material.