He is teen whose childhood was stolen. When you've died twice all before 11 I fear that there's an innocence you and never regain no matter how much bruce might try by making him start public schooling.
Because Dick is more of his dad than Bruce.
He's known Dick much longer.
Dick didn't replace him
He is more accustomed to Dick than Bruce because he's being with the family 3 years [I year he spent making up for his sins, 1 year he spent with Dick as Batman while Bruce was dead, how many months when Bruce lost his memories]
Dick is was the only one to give him unconditional love.
Dick is his Batman
Dick is his mum
Dick is always there for him though Batman might have eyes on him.
Everyone is more comfortable with Dick than with Bruce.