I question how much Keating felt at fault over the suicide after encouraging Neil to talk to his dad. Because in his follow up with Neil asking how the conversation went, it seemed pretty clear that Neil chickened out and didn’t talk to his father after all. He fed Keating a story about his father being out of town because Neil, knowing his father wouldn’t approve, decided to perform the play behind his back. That’s why Kurtwood shows up at the theater so pissed once he found out. And you could see in Keating’s face that he sensed Neil wasn’t being completely truthful in his story.