Children of poverty are more difficult to teach due to the culture from which they come. No one has taken the time to read to them and develop a facility with language, so they have trouble reading. No one has taken the time to teach them how they should behave, so discipline problems are more common. No one has given them a goal to try to reach, so there is little motivation. Add gangs and their influence, the pervasiveness of drugs and the drug culture, and don't forget the "easy" money to be made in drug dealing, requiring no education. There is the welfare culture of dependence on government for living, along with the breakdown in family structure that welfare dependence implies.
Now, since children of poverty are difficult to teach, the best teachers are likely to transfer to suburban schools as soon as they possibly can in order to get out of a failing school and concentrate on teaching, rather than discipline.
Since school administrators are more likely to want to work in a school where success is more easily achieved, the schools serving children of poverty are less likely to be well run. Poorly run schools present a huge challenge for teachers, even when they are the most highly competent and motivated people possible.
And, there are a few heroes who work in schools of poverty for the satisfaction of being able to save a few of their students. They are often vilified for getting crosswise with administration and parents, of course, which thins out their ranks even further.
Then, there is the lack of local control. Children of poverty tend not to do well on tests, even when they have mastered the skills involved. Low test scores bring more control from the state and federal authorities, who have no clue what really needs to be done to improve the situation.
So, there really is no simple reason why the poor do badly in school, nor is there a simple solution to the problem.