There can be many different answers to this, depending on what one sees as the root cause of crime. For example:
It could be because working class people are more likely to be poor. If crime is caused by economic factors, then you would expect people who have less money to commit more crimes.
It could be because of the culture of the people involved. Some theorists believe that there is a “culture of poverty” that causes poorer people to make bad choices. This culture encourages people to do things that might make sense in the short term but can be destructive in the long term.
It could be because the justice system is weighted against such people. A critical/conflict-based approach to American society would say that the society is run by the wealthy for their own benefit. They use the criminal justice system to keep the working class down.
The answer, then, depends on one’s views of the root causes of crime and of the nature of our society.