You have clearly never been poor enough, this statement is just plain stupid. Trust me, coming from abject poverty and being white quite possibly presents more barriers. For starters, some asshole is always telling you how much privilege and advantage you enjoy, and the system is rigged to give anyone who is not a white male preference to education and social benefit programs (you know, because I am white and privileged).
I sincerely hope that no one here or their family ever know what it is like to live in truly desperate poverty, but I can promise you a lack of opportunity is rooted in socioeconomics, not race.
Cody already replied very clearly to this- poverty is indeed a barrier regardless of race, but race is often a barrier regardless of poverty or lack there of.
I guess if we learn anything from that video it is that we as parents must do everything in our power to give our children the greatest chance for success. Do what we can to be/stay married. Dads be there for your kids. We must teach them that they can (and must) be better in all aspects of life than we are. We must teach them that they are responsible for their own actions. That working hard is a fact of life. That there is no place in life for criminal activity.
Seems to me, any child of any color can enjoy white privilege. No doubt there are plenty of black kids that had more white privilege than me.
Sad to say we have not reached a state in the US where all races are treated equally.
It is easy to forget how recently racism was the law of the land in the US. The reality is that people roughly my age (52, MLK was assassinated about 6 months before I was born) are the first ones born as legal barriers to race where eliminated with the successes of the Civil Rights movement. While we know very well not everyone was "racists" (as in KKK), racial bias was of course widespread, much worse in some regions than others.
As with anything, passing a few new laws does not change attitudes or beliefs. We also often see backlash against change. So, many people of my generation would certainly still have been influenced by the pre-civil rights era attitudes. Even if each generation improves, it takes time for biases to be eliminated.
In the same way, those affected by segregation are not going to experience a rapid change. Just as those same laws didn't change all beliefs and attitudes, they did not result in immediate elimination of barriers. It is very reasonable to expect it to take several generations for the impacts of past blatant racism to be overcome.