Your first paragraph is already answered in the post you quoted. Poor people don't do as much to help their kids (this is true) but the post states that the reason they don't do as much is because they don't have the same amount of time to do so in the same fashion as wealthier people (this is ignored). People confuse amount of engagement with level of interest and then ignore the "why".
I don't know if you didn't read it or you just chose to ignore it. The information I quoted included citations. So, we're dismissing citations that say poor people care but believing hearsay that says they don't. Why? It makes more sense to update our understanding of people.
https://www.washingtonpost.com/news...tereotypes-about-poor-families-and-education/
http://www.ascd.org/publications/ed...num07/The-Myth-of-the-Culture-of-Poverty.aspx
For example, here's a simple graph showing that the poor are working much more hours than they did 30 years ago, while the rich are only working slightly more hours.
And studies don't say there are no differences based on race, DNA, culture, wealth, intelligence, work ethic. They say those differences are not what people believe they are. It's basically the human equivalent of learning that the sun doesn't revolve around the earth. We had an idea about these things but more information is demonstrating that our original ideas aren't correct.
Go back to when I first started posting on this forum and I was a big proponent of the "poor need to just work harder and give a damn," ideology. But the more research I've done, the more I've fact checked my own arguments, the less true I've come to realize that to be.
Poor people work hard but they stay poor for plenty of reasons that have nothing to do with work ethic. They made bad decisions when they were younger. They're simply not smart enough to out compete smarter people. They lack the networks to move into different environments. The modern economy has fewer opportunities to move between deciles. Capitalism demands that some people will be poor no matter how hard they work - except "poor" is relative. Poor here is pretty good somewhere else.
The core problem is that people
want to believe that the differences in outcomes are primarily tied to some internal difference or measurable difference. THat it's either genetics or refusal to try that drives these outcomes. And whilte that's part of it. People don't want to acknowledege the elements that drive outcomes that no one has influence over. Things like luck and inherited advantages. For example: Two people are equally smart and equally driven but one person inherits a prosperous company, the other person doesn't. They'll have vastly different incomes and it has nothing to do with race, culture, DNA, work ethic, etc. Maybe the 2nd guy eventually gets there and his kids will inherit a prosperous company but he's never going to have the advantage that his counterpart had, even if his kids do. Or 2 equally driven kids but one's parents are learning the ropes of college admissions as they encounter it. The one kid's parents went to grad school and have been prepping for it since birth. Both kids will go to college but one is on track for Harvard and the other is on track for the state university. By the next generation, their children will be equally prepared but this generation they're not.
People talk about the poor as if it's like a caste system where the poor of today are the direct descendants of the poor from yesterday and their kids will be the poor of tomorrow. Hard working poor people who care about education don't turn into hard working rich people who care about education. Instead, they stay poor but their kids become the hard working middle class and rich people of the next generation.