We know that graphene is the strongest metal on earth. It has very high tensile strength. The inter-planar bonds are van der waals force but the covalent bond across the plane between C-C atoms is what gives them the strength. If the covalent bond is soo strong, then, when we mechanically exfoliate graphene, why does it break into several pieces? It is also said that when we write on paper with a graphitic pencil, many graphene pieces are formed on the trail of the graphite line. Why? If graphene would have been that strong then why would it break?
Graphene is strong per bond, but at the end, it's still a 2D material. The strength of most objects scale with surface area (proportional to the number of bonds), but graphene can only scale linearly.
Also, in the case of a pencil, that's not a pure crystal of graphite, it has defects. Most graphite don't have contiguous layers of graphene running through it.