How and why does sp3 hybridization occur?

1^st consider the bonding in methane, CH4. The carbon atom forms 4 single covalent bonds to hydrogen atoms. However, when we consider the electronic configuration of Carbon (electrons-in-box notation), there are only 2 unpaired valence electrons, and hence there are only 2 available electrons for bonding. Hybridization is the process by which 4 electrons are made available for bonding.
Consider the energy profile diagram of the Carbon atom. The 1^st step in hybridisation is the promotion of one electron from the filled 2s orbital to the empty 2pz orbital. Now all the 2s and 2p orbitals are singly occupied. The 2^nd step is the rearrangement of these orbitals into 4 degenerate sp3 hybrid orbitals. The reason for hybridisation is found in comparing the energy released when 2 bonds are formed versus when 4 bonds are formed. Twice as much energy is capable of being released when Carbon is hybridised than when it is not. Therefore, Carbon is in a more stable and lower-energy state when hybridised.