True story.
I think the problem comes from the fact that "money makes money", but "more money, makes proportionally even more money".

You pick 1000 people with 1000€ each
You pick one guy with 1M€
let them invest etc...
after X years, the guy that started with 1M€ has more.

I think this is true even if all used the same investing strategies, because in our world, liquidity worths money.

Another way easier to understand:
You deposit 1000€ in a savings account, you get, e.g. 2% interest.
you deposit 1M€ in a savings account, you get, e.g. 5% interest.
After one year (simplifying) those 1000 people get 1020000€ and the single guy 1050000€.

Is that fair?