It's not emotionally unstable to be upset with rejection it's the normal reaction (and to be honest there's probably no psychological phenomenon that's been documented more than that). Beyond that I think suggesting it's just "free stuff" shows a complete misunderstanding of what's going on here.

Google is trying to start a movement with the Chrome OS. They're trying to win people over to the thinking that you don't need a desktop. So the dynamics here are more like a political party than a giveaway. As such people are bound to get emotionally invested and their feelings of rejection are bound to be amplified if they are rejected from that movement (imagine a political party that only accepted people's support after an application process)

As I said it's a necessary step because this is a testing process and Google does need a certain profile of person to test. But that doesn't mean it isn't going to sting people if they don't get in.