Why does carbon not form C2 atom with 4 covalent bonds ?
When it form 3 covalent bonds then why not 4 bonds.
The carbon atom requires 4 electrons to complete its octet. In order to do so, it must share 4 of its electrons with another carbon resulting in the formation of a quadruple bond which requires a lot of energy. Consequently, the atoms will come so close to each other that internuclear repulsion will increase to a large value. Hence maximum of 3 bonds can be present between two Carbon atoms and 2 carbon atoms can't be stable by the formation of covalent bonds just by themselves.
Also, Carbon cannot form four bonds with another carbon atom because once they have the triple bond, there's no possible orbit left that would allow one more electron to orbit both the nuclei.
The first carbon to carbon bond is in that plane only. The second and the third carbon to carbon bonds are above and below the ring. The fourth bond (quadruple bond) if formed would be pointing away from the two carbons. In order for this bond to exist, the other three bonds need to be tremendously bent and this is energetically very unfeasible. This strain thus resists the formation of the quadruple bond.