What determines a mineral's hardness?
The hardness of minerals is diagnostic because the hardness is determined by the strength of bonds and the structure of the mineral lattice. Hardness is basically the stress required to create and grow extended lattice defects such as micro-fractures, stress twins, and dislocations.  

Diamond, quartz, and framework silicates, such as feldspar, are hard because they have a three-dimensional lattice of covalently bonded atoms. Native metals are soft because they have close-packing lattices of metallic bonded atoms.  

Hardness is an intrinsic property of a mineral like density or refractive index.