As far as I know, you actually have to get a good way through the main quest before he opens up to you about his past. If you're with the NCR, I think he'll give you the quest once you begin the second mission for Colonel Moore.
Now, I may be wrong here, but I think you need to visit places which'll trigger certain dialogue from Arcade. Off the top of my head, some of these are: Crashed Vertibird, Van Graffs (Silver Rush), and REPCONN HQ.
It's also a good idea to try and gain Gannon's trust. Achieve this by doing work with the Followers of the Apocalypse.