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Women are indicators of quality. If they don't want to go to politics then the politics is not so nice as it should be.

On the other hand here in Ukraine we have many women in high politics but it...

Yep, you already got it yourself. "Человек" in that phrase refer to the Humankind rather than to a male person.

Лучший друг человечества - собачество.
The man(kind)'s best friend is a dog(kind).

I suspect that the ambiguity of this phrase is missed in translation.

I'd say that a woman is man's second worst enemy. After himself. *)