For the case of metals, we observed that metals often have nearest-neighbours in excess of the maximum valency (for example, 8 for Li, which has only one valence electron) and that metals display great conductivity. On this basis, it was suggested that electrons are delocalised over the solid, and we used LCAO (linear combination of AO) over all the valence orbitals to form a band - the 2s band in this case.
The above is from section two in MIT's solid state lecture notes here. They talk about the above two points suggesting an atom in a metal lattice can interact with a large number of others. This then leads to thinking in terms of the orbitals of the "system" or the entire "macromolecule"
However, for non-metallic solids, like diamond for example, bonds are viewed as sp3 localised bonds and the number of nearest neighbours equals how many covalent bonds it can form, and it has poor conductivity as well. The poor conductivity is often explained by saying the band gap($E_g$) to the conduction band is large. But I don't understand the meaning of forming a band in this context, when the assumption we used of delocalised electrons over the entire solid doesn't hold.
Also, the description for the formation of the valence and conduction band for diamond is given in terms of sp3 orbitals combining to the form the bands. Why is hybdridisation (from VBT/VSEPR) being brought in to the picture here?