The "official" version, or as official as we're ever going to get, is that he left because he didn't agree with Steve taking over the production, and wanted to explore different types of music. Maybe if Steve conceded and the whole decision making process in Maiden was a little more democratic, he would have reconsidered?
Huh. I've never heard that before.
In the book he also says that he read whatever inspirational quote about leaps into the unknown (don't remember which one at the moment), and that made him realize that as long as he was in Iron Maiden, he had that cushion, that parachute, something to fall back on, and if he wanted to be taken seriously, he had to leave Maiden, a "burn your bridges, don't leave a plan B open" kind of situation to push himself.
He did want to do other stuff, and definitively wasn't happy with Maiden's then recent outputs (when he came back, after all, he insisted for an external producer and a good studio), but he realized that doing side stuff while still being Maiden's singer wasn't challenging enough and so he felt he had to go.