Why tell him the boy did it?
He tells nikolai that he's figured out that he killed his foster parents at 12 years old, but what was the point of it? Teddy was already a bad guy, so we didn't need any convincing. So why tell him this story?
shareIt had nothing to do with making him a "badder" bad guy, it was McCall getting in his head, playing mind games. McCall did his research. He tells what is ostensibly just a story, never actually overtly stating he's talking about Teddy (though they both know he is) and then tells him he think the boy did it and why. This is coming straight off the back of Teddy giving him his "When you look at me, what do you see? The answer is nothing. I have no feelings about you one way or the other." and launching into what an emotionless badass he is in an attempt to intimidate him. McCall is using the story to say two things:
1. I see everything. I know who exactly who you are.
2. You aren't emotionless. You're driven by fear.
The tl;dr of the scene is:
Teddy: I'm a mysterious boogeyman. Boo!
Bob: You're not the boogeyman. You're not mysterious. You're a pussy. GTFO or die.
It clearly works to some extent because he clearly becomes uncomfortable as he tells him the story and feels the need to reiterate "You know nothing about me", but he's out of game. He's got nothing.
excellent response
that's basically how I saw it as well