Only thing I can think of to add is a comparison to China. They say there is a rare but periodic horrific crime of Chinese men attacking school children with knives (as guns are so rare). They stab as many as they can.
Seems what they all have in common besides mental illness is extreme unhappiness and hatred of society. Makes me wonder and guess he has that trait; A hatred of our society and striking out at it at our most vulnerable and cherished. The ones most likely to hurt the society he hates so much.
Guess it seems plausible?
He was being chased and it was fate that he ended up at that elementary school.