The premise of market indexes beat 50% of investors is a way underestimate. The real number is well over 90% closer to 95%.
Where I am from that is more than good enough an answer, but I can see how that is less than satisfying.
So allow me to elaborate.
Actively managed funds (by professionals) rarely beat the market over the long term (5-7 years). In fact, they rarely beat a monkey with a dart board.
Warren Buffett actually explained it really well.
The simplest reason is, modern portfolio theory.
For an individual investor, having one great investment idea is HARD. Even with a team of professional, having 3 or 4 great ideas a year is very difficult. Warren Buffett said there were years he bought nothing because there was just nothing to buy.
And notice, the more positions you have, the more companies and business sectors you will need to follow.
It is essentially impossible to have that many great investment ideas, and even more impossible to track them all.
But modern portfolio management theory says, you MUST diversify.
Logic dictates, the more you diversify, the more duds you would have.
BUT unfortunately, your funds are limited. So no matter how diversify you are, you would never be as diversify as the market.
But wait, there is an even worse part of the theory, which says you should take profits just because it has gone up "too much" ... This leads to the bizarre scenario where people sell the winners too soon, and hold the losers too long.
As a result, by adhering to the modern theory of portfolio management... almost nobody beats the market.
And finally, the market is not the median of investors.. the market is all the stocks......