There are a lot of factors, but AFAIK the main dynamics are:
- We primarily fund schools through states (federal funding is < 10% on average)
- States are largely funded via regressive taxes (like sales and property taxes)
- Until Trump's tax law this was all deductible from federal taxes. Now it's just property taxes and it's limited to $10k (which is pretty high, we're talking a $333k property w/ 3% property tax)
So effectively what happens is everyone pays a flat tax to fund schools, then people wealthy enough to pay income or capital gains taxes get their school payments subsidized by the federal government.
It's also important to note that many private schools are religious and pay no taxes at all. They also receive lots of federal benefits via federally funded and run intermediary organizations. Finally, charitable giving to religious organizations (including schools) is tax deductible.
The effect of all this is a huge education subsidy for high income earners and the wealthy. Couple this with the total lack of redistributive policies for educational funding, and you get what NPR calls "a money problem" [1].
And if education is the silver bullet, what we're counting on to lift people out of poverty, and what we point to when we talk about "equal opportunity", then the future looks dim indeed.
[1]: https://www.npr.org/2016/04/18/474256366/why-americas-school...