Confusion regarding sigma bond and pi bond

I was recently told that a sigma bond between two $\mathrm{3p}$ orbitals is possible but a $\pi$ bond between the same orbitals is not possible.


Although I was not told the reason, I am speculating that a $\pi$ bond between them is not possible due to a comparatively larger size in comparison to $\mathrm{2p}$ orbital.


Is it the same reason why $\ce{S2}$ does not exist?


Can someone confirm the theory and give reason for the same ?




The most common explanation for the poor multiple bonding in 3rd row main group compounds is poor orbital overlap due to the radial node of the 3p orbital. 


Since the 2p orbitals have no radial nodes, the lobes can overlap in-phase to form a reasonably favorable bonding interaction. The radial node of 3p orbitals makes it so that when the outermost (most overlapping) parts of 3p orbitals are overlapping in-phase (stabilizing), the part that penetrates into the inner parts are by definition out of phase (destabilizing). Hence the overall interaction is much, much weaker. Bonding through 3p orbitals are much more favorable when they are more end-on than when they are side-on like in multiple bonds. Hence, $\ce{P4}$ is much more stable than $\ce{P2}$ and $\ce{S\_2}$ is less stable than larger sulfur cycles.


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