Reminder: Talent is a variable; technique is not. Bradley Cooper is a talented actor, but in this scene he didn't use what I would assume was his training at The Actors Studio. That is, that every drama is a series of progressive actions and therefore, that in each succeeding scene, the actor must choose an action/need/objective; using a simple sentence with a verb, in order to avoid a narrative performance. As well, the actor must understand dramatic structure well enough to know that when exposition (backstory) is part of the forward action of a scene, the actor must avoid the trap of narrative, and choose an action in order to dramatically perform the scene.
The character's need/objective in this scene is to convince his psychiatrist that he doesn't need to take meds. Consider the previous circumstances: (1) His mother insisted he go with her to therapy and threatened him: "You have to go. It's part of the deal. You can't live with us and not go." (2) When he entered his psychiatrist's waiting room, his dreaded song was playing, which made him aggressive in a way he knew was harmful to staying off meds, and now, in the above scene, he must convince Dr. Patel, regardless of his behavior in the waiting room, that he doesn't need meds. This scene is pure exposition and as written, is information that has already been discussed (probably many times) between Dr. Patel and the character. Unfortunately, Mr. Cooper described the backstory, which is narration, not drama, and although he read the scene intelligently, it was still, nevertheless, a reading of the scene, and not dramatic.
For example, "...I'm not the explosion guy, okay? My father is the explosion guy," is a reminder to the doctor, it's not new information for the doctor, and is said now again in support of not needing meds. "He got kicked out of that stadium he beat up so many people at Eagles games, he's on the exclusion list," is again, old information for Dr. Patel, and is also progression (more information) of the argument against needing meds. Since this is old information, a necessary reminder in support of his argument, it needed to be emphatic; it could even have been delivered ironically, considering the primary need to convince the doctor. From then on, as he says, "Let's go back to the incident," he is going over details in order to try to justify his prior behavior, and with the aid of the doctor, recalling for himself the pattern of his prior behavior, the specific history that doesn't justify not taking meds. The actor needs to realize that he's joining the character in a journey of discovery through a series of rising actions; he is not telling a story.
When technique isn't practiced throughout, the talented actor will present an uneven performance. There will be scenes in which he seems to work correctly, because, accidentally, he has been able to connect with the actions -- something about the scene resonated deeply for him, but, in scenes where this was not the case, he'll revert to indicated acting -- to showing us the character.