In the book The Kite Runner it stands to reason that when his wife came clean about her past and shared her woes that it would have been a great time for Amir to share his situation as well. However, Amir was emotionally still ashamed by his childhood actions and inaction. He carried so much guilt inside him and shame that he could not have told the girl he loved the story.
IN addition, Amir was raised by a father who was from Afghanistan and his values and the way he was raised had to be influenced by Baba. The men from the country are not usually used to sharing their feeling with women and Baba had no way and also was known to keep all his feelings inside about her. Amir was also very ashamed about the incident in relation to his father so it would have been difficult for him to risk opening up with anyone.
Amir waited until the time was right for him. I would have to say sice he was not ready, he made the right choice not to tell.