I do not really care anymore, but it would have been a cool experience to go to a good school.
In the case of Caltech, they may have looked at your major and decided that they wanted less Foo majors and more Bar majors. All about recruitment. Either way, I'm sure someone argued your case, as brandnewlow commented.[1]
For every candidate they accept in general, they must reject 8 others.
Not necessarily. Would you be okay with being the dumbest person in the room, not just for one class or one semester, but for four years? A lot of smart kids go to CalTech, MIT and Harvard, but end up dropping out and finishing their degree somewhere else because they're not accustomed to failing on a regular basis. Unless you're convinced that you'll be able to handle repeated failure (because it'll happen when you're trying to achieve at that level) that sort of school may not be for you.
Then there's the fact that these schools are expensive. So not only do you have to be able to deal with failure at an emotional level, but you have to be able to deal with failure financially as well. If you don't have the budget to repeat at least two or three classes - don't bother with a top-ten university.
this of course assumes I want to be good at whatever the subject of the room is.
Kid's take time off after repeated failure, but they often come back once they're off of academic probation. Others will leave to take jobs, start companies, or transfer to a similarly ranked school that they simply like better. I've heard/seen tens of these cases, but never one where students purposely transfer to a school where they're less prone to fail.
Moreover, financial aid seems generous here. And private school prices anywhere, regardless of the caliber, are very similar.
If anything, take solace from the awkward social life, the excessive workload that makes entrepreneurial endeavors seemingly impossible, and the fact that you really don't need a good school to succeed.