# Why are homonuclear diatomic molecules non-polar?

Because the elements that comprise a homonclear halogen molecule, ${X}_{2}$, clearly have equal electronegativies.
A homonculear diatomic molecule, ${X}_{2}$, is composed of 2 halogen atoms, which have the same electronegativity. Given this, there can be no charge separation, and no possibility of polarity in the $X - X$ bond.
Molecules such $I - C l$ or $F - B r$ can certainly exist. Such molecules would exhibit a dipole as there would be unequal sharing of electron density.