Short answer: Actively managed funds do worse because they have more overhead - money managers cost money, and, on average, they don't bring in more money than they cost.

There's also the whole thing about the market not being quite efficient. If you can outperform the market, you can use the same strategy with more money in order to make more money, up until you start trying to buy and sell enough stock that you actually change the market. As a result, the people who are best at predicting the market will control it, and it will be efficient. But it has to be just inefficient enough to pay them enough to keep doing it. The same amount of money would have to come from other people trying to predict the market and failing. As a result, an average person would have a small expected loss that goes to those people, and if the actively managed funds are just hiring average people, they'll lose money.

This makes sense. It's like playing poker at a raked table: the "average" return of playing poker at an unraked table is zero dollars, because every dollar that someone wins is also a dollar that someone loses, but at a raked table, the house gets a cut of each pot, so the "average" return is negative. Similarly, every dollar of "above-average returns" earned in a market has to have a corresponding dollar of "below-average returns". However, actively managed funds are like playing in a raked game: the money managers have to get paid, so they have to do better than average in order to earn "average" returns for investors.