Sony decided to be clever and try to release the PSP "midway" through the GBA's lifecycle.
That way, the GBA is a success and all, and Nintendo would be crazy to abandon it, but Sony can look all shiny and new with cutting-edge technology. Then by the time the GBA is done, and Nintendo wants to release the GB-Next, the PSP won't be cutting-edge anymore, and the GB-Next will be more shiny and new, but Sony can claim to be all "established" and "successful". It's what happened with NES-vs-Genesis-vs-SNES. There's more of a fighting chance than if you went head to head with either the GBA or GB-Next. Same markets. Different timeframes. You're likely to get 50% marketshare by default.
But, Nintendo's smart, so they made the DS. It's funky and weird, and it lets Nintendo and the third parties get all creative (which is something they say we need), which makes it different enough so they don't have to "give up" on the GBA, while at the same time it's all shiny and new, and can compete with the PSP.
Nintendo has said that the DS is not "the next GBA", and that they're even working on a new GBA which will be "philosophically similar" to the GBA (meaning not so funky and weird).
If you're cynical, you can infer that they're just "saying that" to keep pressure-to-perform off the DS, or trying not to lose face, by making a new handheld early because "Sony forced them", or maybe they're just trying to get the forward-viewers who are drooling over the PSP's measurements to look even farther, and see what could be made even better, just a year or two later, so they lose interest in the PSP.
But no matter what their plans (or lack of plans) are, the performance of the DS and/or the PSP and/or the NGage (success, failure, or some weird mixture) will cause any plans for a GB-Next to be re-evaluated on-the-fly.
(I'm betting that the eventual GBA2 will be a portable GameCube called a "GameBoy Cube". Predictable. Decidedly non-funky.)