Diamond is made of carbon atoms attached rigidly to each other in three directions making diamond very strong. graphite, as found in a pencil, is easily broken under pressure. since graphite is also made of carbon atoms, why might it have such a different property?

In diamond, The arrangement of carbon atoms follows a tetrahedral shape. Each carbon  is attached to four other carbon atoms, forming strong covalent bonds.This  arrangement of the diamond is very durable and rigidity, that's why is necessary so many energy to break it.
On the other hand, graphite, has a different geometric arrangement. the carbon atoms are arranged in 2D sheets and each carbon is linked to three other carbon atoms, forming hexagonal rings that are easily broken.

A.