In this excerpt, Junior is making several implications about his family's outcome.
First of all, he is fighting the common assumption of poor people having no plans or dreams, or any intent to stop being poor. This is a myth that is often perpetuated by society, even though it is rarely the case. Junior argues that his parents in fact did have dreams about getting out of poverty, even though it never happened.
Secondly, Junior is saying that the reason his parents were never able to do it was because no one ever cared about their dreams. The implication is that no one can achieve his or her dreams if they are not given the chance to do so. And poor people are given very limited opportunities in life.
The overall intention is to show how much of his parents' misfortune was not due to their lack of vision or intent, but due to the lack of opportunities they were given. It is a criticism on a social system that gives few opportunities for advancement.