Probably because his family didn't take as much interest in him as they did to his elder brother, Richard. John may have had a bad childhood and wanted revenge on his family, but I'm just guessing here.
This might help:
"King John and his nephew Arthur
Arthur lived at the French King's court, and when he was sixteen years old, Philip helped him to raise an army and go to try his fortune against his uncle. He laid siege to Mirabeau, a town where his grandmother, Queen Eleanor, was living. John, who was then in Normandy, hurried to her rescue, beat Arthur's army, made him prisoner and carried him off, first to Rouen, and then to the strong castle of Falaise. Nobody quite knows what was done to him there. The governor, Hubert de Burgh, once found him fighting hard, though with no weapon but a stool, to defend himself from some ruffians who had been sent to put out his eyes. Hubert saved him from these men, but shortly after this good man was sent elsewhere by the king, and John came himself to Falaise. Arthur was never seen alive again, and it is believed that John took him out in a boat in the river at night, stabbed him with his own hand, and threw his body into the river. It is believed that John was guilty of his nephew's death, and he was fully known to be one of the most selfish and cruel men who ever lived; and so lazy, that he let Philip take Normandy from him, without stirring a finger to save the grand old dukedom of his forefathers."
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