If I have money in my family, I can go to a private school, then an elite university, pay for additional vocational training, then take an unpaid internship - possibly at a business owned by my family - while living with my parents. I can then land a cushy job and become rich.
If I'm poor, I can't go to university or end up in loads of debt if I want to, then I can't afford additional training and have to start earning a basic wage straight away. I will have no familial connections and very limited opportunities for bettering myself or earning significantly more money.
I could be rich and stupid and lazy and still end up earning a vast amount of money, and I could be poor and smart and hard-working and never be able to earn enough money to get by. If I'm born rich, the chances are I will continue to be rich and may one day be paying poor people who are smarter than me.
If you work really hard and look for opportunities, you might be lucky, but even if you're just as motivated as a rich person, you'll be very unlikely to earn as much as you would if you were born in wealth.
Without writing a tonne, if you're born in poverty, you could be smart and gifted, but your cultural circumstances will very likely prevent you from ever attaining your potential. What are the chances that someone who could be as great an astrophysicist as Stephen Hawking was born in a poverty-stricken country and never had the opportunity to achieve his potential? Well, almost certain.