The reason there are no stable quad bonds between carbon atoms is due to the number of atomic orbitals available. Carbon has four valence electrons, which occupy its 2s and three 2p orbitals. In order to form a bond, two atomic orbitals must overlap. To form a double bond, two pairs of atomic orbitals must overlap, and so on. However, there are only four atomic orbitals available in carbon, so it is not possible to form a quad bond, which would require four pairs of atomic orbitals to overlap.