Not having money does make it hard to be a good parent: having time to spend with your kids instead of working a few minimum-wage, non-school-hours, part time jobs, encouraging them to explore and learn about things they find interesting and funding this exploration as necessary, providing safe places to be and healthy lifestyles are all hard to do when you're poor.
Clearly, having money doesn't make you a good parent. And you don't have to have money to be a good parent. But it does undeniably have an impact on the statistics.
Agreed, but also I think expectation, confidence, ambition are as important as opportunity. We have some relatives, from the outside they look like a totally normal middle class loving family. But we saw time and again the parents talk like, daughter is the smart one, son is the not-so-smart one. Telling him his teachers are idiots etc. They just set that kid up for failure and it was difficult to watch.
Clearly, having money doesn't make you a good parent. And you don't have to have money to be a good parent. But it does undeniably have an impact on the statistics.