18-year-old Abel Cedeno is charged with stabbing 15-year-old Matthew McCree last month.
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Cedeno was initially charged with murder, but claims he acted in self defense.
McCree's family will be suing for $25 million in damages.
The stabbing happened inside a classroom at Urban Assembly School for Wildlife Conservation in the Bronx
SCENE PHOTOS: Deadly stabbing at NYC school
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Attorney Sanford Rubenstein, who is representing the victim's mother, questioned why two teachers in the classroom were "standing there and did absolutely nothing" during the attack.
He also questioned why the NYPD and school officials did not see a need to install metal detectors until after the stabbings, calling that one of the "serious legal issues involving the Department of Education and NYPD school safety division."
There was extra security and metal detectors at the school after the double stabbing -- the first fatal incident inside a city school in 25 years.