As you noted, that is a generalization. There are millions of middle class and wealthy black families and millions of poor white families.
But why is that called 'white previledge'. That is not a previledge. It is a tragiedy that we have crime-ridden inner city ghettos with schools in those neighborhoods which are not conducive to education. It should be called what it is, not some term which creates even more racial division than there already is. The idea that it is the white man holding people down and we have a society where only white people succeed is the mentality that has been peddled is counter-productive. It is not white previledge which makes the ghettos so dangerous and the schools there a complete crap show. It is not white previledge which causes 66% of black children to be raised by a single mom. It is not white privildge which cause black males to commit 6 times more violent crimes.
The media does not help. They continually focus on racism and white on black injustices. That is still a huge problem, but this creates a myth in the minds of many blacks which makes them scared to integrate into better neighborhoods. We have made all kinds of laws and have educated people for decades protecting the rights of blacks and reducing racist sentiment. Maybe we are only 80% there, but where we are today is light years from where we were 50 years ago. The problem is, we are not going to make a dent on that last 20% by forcing them to change. The way every minority in history has ever gotten acceptance is to change those statistics above and that will never happen by blaming whites.
I do not know the answers, but the answer is not what we are doing. It is not to continue to only focus on things like institutional racism, white previledge, racial profiling. There needs to be a new focus on improving pride, family, community, and hope. There needs to be instilled a sense that blacks can succeed in this system. The primary focus now needs to be within the black community.