2 Works in Teacher Tom Riddle
James and Lily got divorced, leaving Harry forgotten in the wake of their broken up family. Luckily the teenager has Mr. Riddle, his History teacher, there to make him forget about his misery.
Harry didn't really think before he tried that toad and chicken egg thing and now he has a baby Basilisk with him at all times. Out of everyone to let in on the secret Tom Riddle seems the best choice.