Not saying it's a solid plot, but news of the enclave could have gotten around, particularly with James being in the wasteland before entering the vault, as well as him being extremely resourceful and connected with Rivet City, I'd imagine he'd have significant distrust of their intentions - despite their eyebots I get a general lack of trust for them, especially considering the BoS presence and their little disputes with The Enclave, and James having a history with them as well, as well as the possibility of the story of the chosen one becoming legend and moving throughout the wasteland (it did in NV), I find it perfectly reasonable to presume that James had a decent amount of knowledge of how untrustworthy they are.
All of that aside, it's also possible he didn't trust the Enclave's scientists or indeed was generally very anti-authoritarian (wouldn't surprise me considering how chuffed he was to leave the vault, and how he expected the overseer to go crazy) and didn't trust anyone else to handle it. Alternatively, he might have simly been power hungry, but I doubt that.