Because he played Robin John Blake (he preferred not to use the name Robin and just went by the name John Blake) in The Dark Knight Rises and when Bruce Wayne fakes his death he passes on the knowledge of his Batcave thus inferring that "Robin" takes over the crime fighting.
But the fact that his name is Robin, does make him Robin. They never say "hey this is the green and red wearing Robin " they tease it with the Nightwing colors but its more of a nod than anything.
Nope, the first Robin was Dick Grayson, who then became Nightwing, then was Todd, who was killed and resurrected, and then Tim Drake, who became the Red Robin (aslo known as condom man to Damian Wayne) and then Bruce's son, Damian, who was also killed. But I get what you're saying, let's not talk about X-men origins, its a sore point x_x
May I remind you... *whispers* X-men Origins...
And I'm glad I made a point (●__●)