While capitalist society has no laws to prevent mobility up and down the class scale, in practice it may not be easy. Your book noted that less than half, but a significant number of people move up in the income scale, relative to where their parents were. Most people do not move very far up the scale, either. They may move up one notch, but it is rare to move from the very bottom to the very top. Please give some specific examples.
Marxist theorists talk about lots of issues.
Also, wealthy parents can spend more money on their children, which certainly gives them an advantage over poor children. Health, and the ability to pay for medical care or live in safe neighborhoods is also harder to come by for lower income class families.