Early in The Dark Knight Rises, when John Blake is talking to Bruce Wayne he reveals that
he knows Bruce Wayne is Batman.
He says he figured this out because
they are both orphans who lost their parents due to crime, and he can see the pain in Bruce Wayne's face.
While that makes sense, I don't see how that led him to realize this. Did I miss something?
His monologue in that scene pretty well explains what led him to figuring out that Bruce is Batman. On a more thematic level, Blake himself took a similar path as Bruce, he's channeled his anger at losing his parents into fighting crime. However, as Blake didn't have Bruce's resources, his options were more limited.
When it came time to train to fight crime, Blake chose the path that was available to him, he signed up to become a cop. With Bruce's resources, he traveled the world to train, before ending up with the League of Shadows. Then he expended his money buying and building the Batman suit and equipment.
Blake had a similar enough background as Bruce, and reacted in a similar way to the loss of his parents that he was able to deduce that with more resources, he would have become the Batman.
