Think about it this way: investors buying index funds are doing about as well as the market. Active traders who beat the market do so basically at the expense of other active traders who do worse. The aggregate performance of all active traders won't beat the market. However, there are extra expenses (overhead, fees, etc.) to active trading, so we actually expect active traders to perform worse.

The second issue is taxes. A passive investor gets to pay the long-term capital gains tax after the stock is sold. Someone who actively trades is getting hit with a short-term capital gains tax (paid every year), which is considerably higher and will positively murder one's compound interest rate.