Well I can't speak for everyone, but I can speak for myself:

More than the "rights of the rich", I care about the rights of people to BECOME rich. Sadly, once people become rich, they often use the political power of their money to slam the door on others, so that they and their families can stay The Rich for perpetuity. The world is no better off thanks to John Kerry, even if his wife's great great grandfather he invented ketchup 100 years ago. But the world is a LOT better off because of Elon Musk inventing practical electric cars, economical space flight, and low latency satellite internet, or because Jeff Bezos invented modern e-commerce.

If there's no opportunity to become rich, then the country becomes reified with a couple of families owning everything and no innovation - as it is in Italy or Canada. Everyone suffers as a result.

Why are rich people often libertarian, well, this is a bit of a self-serving point of view, but I think SMART people tend to become rich, and smart people also tend to become libertarian. There are rich socialists, like John Kerry, but these are Old Money rich, they did not contribute anything to become rich, they only became rich by inheritance.

So really, libertarianism is not so much the philosophy of The Rich as it is the philosophy of The Disrupter. And disrupters are the ones who move the human race forward.