This is mainly because rich can choose between many different options through their lives. Rich can afford to waste their time, waste money even. Things are always more easy for rich. You may have wrong investment but quickly solve it through many different correct investments. If you are poor you generally get 1-2 or 3 at best chances in life to leap forward. Otherwise you will stay poor spending your life for money. I personally don't think poor gets poorer (Today's poors are always richer than past). But rich definitely stays rich.
If a person is born into a rich family, then from birth he thinks differently, he sees the example of his parents, he has an excellent role model to become rich in the future. The rich give their children the best education, they get a good financial education and are more likely to have good start-up capital for their businesses or investments, and they are also more likely to inherit their parents' wealth.
Something similar happens to the poor, they will give an example of a poor life, to some extent, children imitate their parents, copy habit, and as a result, the circle closes. It will take a very big effort to change, because wealth starts in our heads.
This is something irrelevant but I've seen a quote from an anime saying "children who are born in war wouldn't know what is peace, while children who are born in peace wouldn't know what war is", in reality what you have said is right that your living environment can hugely affect a person's point of view toward things, along with traditions and norms you that is common in your are will be molded into you and would be forever with you. Though I've said that this is irrelevant, somehow we could see some reference in terms of economical situation in which, it will take a lot of courage for someone to escape poverty by putting his mind into it and actually doing the grinds for it,
compared to rich people who could fall anytime. One slight mistake about disregarding financial management, it will cause a lot of problems for rich people but atleast they can recover that easily thanks for their spare assets. The poor? Not only they would consider changing the way they approach money, but the pressure of thinking one slight mistake would be the end of all is also along their lines.
Escaping ones poverty is never that easy, and I myself is a living witness on that. It is not that you wanted to be rich but a life that is worth living as an average earner is what most people want, who would hate that? Of course no one.
You made a very important remark there. It is the ability to cope with problems, drawbacks, the capacity to absorb negative events without having to cope with the full range of negative consequences. You could apply that to almost any negative circumstance you can come across in life.
You need an outstanding lawyer? Money will solve it. You need an outstanding doctor? Money will solve it. You need an outstanding equipment because you have an outstanding talent like racing or horse riding or anything else that is expensive? Money will solve it and you can benefit from your own talents. Some people can't even benefit from their own talents for financial reasons, which ultimately means you have no time to pursue your passion and your talents because you have to go to work while a rich kid can take lessons learning the violin with the best teachers available.
Or there is an idea you have but you have only one shot. Perhaps you have two ideas and you have to make a decision to pursue one of them and let the other one go.
The list could go on and on, but I must say that sometimes starting poor can also be an unbeatable catalyst for success. If you are going your way and you have made it quite far and you compete with a rich kid on the same level as you, you are probably more eager to put in more work than the rich kid. You are used to rough situations. But the average shows that rich and well educated people outpace poor and poorly educated people.