I have a friend with a kid like that. He's a psychotic demon child for her (and a normal kid for everyone else-- I would not believe the stories she tells me if I did not hear them play out over the telephone and occasionally see them).
His Dx is ADHD. Everyone who believes THAT'S the cause, stand on your head and crow like a rooster.
I will not find fault with other parents that I do not know personally.
I will say that what my friend's kid suffers from is verbal abuse, extremely erratic parenting (a mother who alternates between screaming threats and epithets and kissing his ass), and being spoiled stinking rotten.
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"Alas, our dried voices when we whisper together are quiet and meaningless, as wind in dry grass, or rats' feet over broken glass in our dry cellar." --TS Eliot, "The Hollow Men"