faculty brat
A student who's got a teacher for a parent and somehow thinks they're the best student in the school.
My kid's a faculty brat. He's my student and he's my kid, and he thinks he's the best in the school.
She's a faculty brat. She gives me attitude and still thinks she's the smartest kid.
He's a faculty brat. He texts me during class and says I'm the worst teacher ever.