I would consider, "rich" and "elite" two different things. Someone who is elite very well might become rich, and might consider themselves better than others because of their special degree of knowledge or ability in a particular area.
A rich person needn't have done anything to become wealthy, and by getting what they desire while others don't because of nothing other than their wallet, they may presume it is a measure of social worth. These examples pretty easily stand out. Paris Hilton or Kim Kardashian comes to mind. Of course, they come with the baggage of our warped celebrity culture, but I mean even before that.
But why do the rich think they're better than the rest of us? Why does anyone (and everyone) think they're better than some other people, even if they don't want to admit it? Because we're all biased toward our own self interests, and can't possibly understand anyone else's situation as well as we think we understand our own.