Every time I try to answer this question I get the post auto deleted.

In short it started because that is the only real physical difference between most anunnaki men and humans.

So when humans started serving under them as priests and priestess, they started imitating the gods and removing the skin.

But what really made it main stream was the anunnaki women, they would take human male slaves for their entertainment and force them to have one so they wouldn't get grossed out.

This also caused the noble class to do it as well so they might have the chance to create a demigod.