Visibility of the whites of the eyes conveys significant social information. You can tell where a person is looking as well as their emotional state (fear, surprise, anger, etc) just from looking at the whites of their eyes. Humans are the only primate species that have significantly visible sclera (eye whites).
The clarity of the whites of the eyes can also convey significant information about the health of a person, which may be important during mate selection (don't pick someone with discolored sclera, they probably have something fundamentally fucked up with them, like hepatitis or something).
It's perfectly normal to find someone who's eye whites you cannot see to be in some way abnormal and not trustworthy. You can't tell what they're thinking, feeling or focusing on... they are shifty.
You misunderstand. No one in the world has black 'eye whites'. He means the iris.
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