I think you want to ask why carbon does not form four bonds with another carbon atom.
Carbon cannot form four bonds with another carbon atom because once they have the triplebond, 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 tocarbon bond are above and below the ring. The fourth bond (quadruple bond) if formedwould be pointing away from the two carbons. In order for this bond to exist, the other threebonds need to be tremendously bent and this is energetically very unfeasible. This strainthus resists the formation of the quadruple bond.
However, you must also note that C2 is very well existing. In your higher grades you will bestudying molecular orbital theory which will explain it to you the formation of C2 bond aswell its diamagnetic nature.