Why is my ♦ hammer (i.e. diamond) so durable, but it can burn?
It is bond strength, not hardness, that determines how easily oxygen
  can attack and burn a material, allowing me to burn a diamond in a
  pool of liquid oxygen resting in a block of graphite.


Diamond is hard because its bonds form an inflexible, three-dimensional lattice. However, the strength of these bonds themselves is not even as strong as graphite, for example. Graphite has much stronger bonds, but they create "sheets," which can slide around, making graphite softer but harder to burn.

(source)

Indeed, people have burned diamonds before by putting them in tubes of pure oxygen.