If graphite's just a huge polymer of benzene why isn't it an aromatic compound (polymer?)
Graphite/graphene is aromatic. The first image below is a common crystallographic representation of graphite and does not account for covalent bonding.  The second one shows the molecular structure of graphite as a kekule representation. Graphite is made of planar sheets of carbon atoms in 6-atoms rings with conjugated double bonds. This also satisfies the 4n+2 π electrons criteria needed within the aromatic ring for graphite to be aromatic. This aromaticity is why graphite is not only stable to high temperatures but also a more thermodynamically favorable allotrope than diamond under typical conditions.


Crystallogrphic Representation of Graphite.


Kekule Representation of Graphite.