54% of adults lack proficiency in literacy
Public schools have failed to “educate”
It means "school paid for by taxes", which, as a European is probably the sort of school you attended
Private school is a school you have to pay to attend
The distinction between public and and private that British English historically had was useful too. State school is more accurate too (its distinguishing characteristic is state control and funding).
I also think the old (probably a century ago, or decades ago) "privately education" is a far more accurate description of what is now called "home education" in the UK and, even less accurately, "home schooling" in the US).
I can't find any data that supports this causal assertion, and I can find plenty that contradicts the premise that US literacy rates have reduced since compulsory education began.
Citation?