Let me be very clear.

Lightness of skin has long been tied to priviledge in a color caste system where whiteness is on top.

Hatred out of jealousy towards lightness only reinforces the superior (white to light) inferior (brown to dark) dynamic.

To be hated on because everyone (speaking very generally of course) wants to be you or like you is VERY different from being hated on because no one wants to be you or like you. These are 2 totally different social dynamics.

Side not, in a book called the Color Complex (if I remember correctly) it stated that 40% of black parents seeking to adopted specifically requested light skinned children. The amount requesting darkskinned children were negligible. Regardless of what these parents look like, it says something about us that in a community with a rainbow of hues that almost half of those who COULD pick the complexion of their child choose light.