Depends how rich we're talking here. But basically, when you have money, you can use it to make more money. If you don't have money, you're stuck working all day just to get by, and even if you save responsibly, you're probably never going to get to the point where you can invest enough to be rich.
Wealth is considered a measuring stick for how much of a person you are, and especially for men. So if you're working your ass off all day just to make ends meet, and Richy Rich is raking in millions a year and spends most of his time on the golf course, yet everyone still thinks Richie Rich is just a higher quality person than you are ... I could see how that would get on peoples' nerves. Esepcially if Richie starts talking down to all the people, "Let them Eat Cake", kind of how the rich often do, since they're wildly out of touch with the idea of working for a living and think everyone just has millions sitting around to invest, but are instead blowing the money on drugs, cars, women, or whatever.
Not to mention that he who controls the money has the power to prevent others from becoming wealthy .... you'll notice that rich families tend to stay rich, and poor families tend to stay poor.