The intuition behind carbon's covalent bonds As an introduction to hybridization, my textbook discusses that "The formation of covalent bonds often starts with the excitation of the atoms." Taking carbon as an example, the author says:


  Carbon  forms four covalent bonds. Yet if we consider the elctron configuration in the carbon atom, we would not predict this as it has only two singly occupied orbitals available for bonding. ($1s^2\, 2s^2\, 2p_x^1\, 2p_y^1$)


I don't understand why carbon's bonding is counterintuitive. Why don't the 4 added electrons just go into the $p_x$ and $p_y$ orbitals then into some newly formed $p_z$ orbital? Why does the existence of "only two singly occupied orbitals available for bonding" complicate things? 

As an extension, why is the excitation of the s-orbital electron to $p_z$ needed?  

Thank you for your answers and please try to respond keeping in mind that I am a high schooler (more specifically, part of the IB Diploma program).
The most naive answer would guess that since every orbital wants two electrons and there are two orbitals with only 1 electron in each, then 2 more electrons are needed. 

However carbon typically combines the one $2s$ orbital and three $2p$ orbitals to form four equivalent $2sp^3$ orbitals each with one electron. The four hybrid orbitals have a tetrahedral shape. So after hybridization, the carbon atom wants to create four bonds to fill the four electron shell vacancies.