Where do you live? The private schools may also get funding, and public schools have much higher expenses for special needs students etc. who are often not allowed to enroll at private schools.
Several private schools I know in west coast burbs get by on <$10k and actually have higher staff ratios and more autistic kids than standard schools (many parents need the refuge because the public schools are especially ill-suited to the needs of many families with kids on the spectrum).
The point, though, is that there is an incredible amount of bloat in the public system. Funding amounts themselves are not a primary problem, though perhaps allocation of funding is!
It's not hard to find examples of inefficient spending in education (the depiction of Newark Public Schools in "The Prize" is particularly poignant), nor is it hard to find examples of dramatic underfunding (just ask any teacher in a low income area). But anecdotes on either side of the equation don't really lead us to correct policy.
There are costs to operating a school district that have increased dramatically in the past 30 years (most significantly: employee benefits, special education compliance) and have not been met with comparable increases in funding. Additionally, we've dramatically raised the expectations we have for schools (holding schools accountable for "No Child Left Behind" and raising the rigor of instruction with the Common Core & new assessments).
From this vantage point, it seems clear to me that we need to either narrow the scope of what we ask schools to do or increase funding to meet additional burdens. And it'd be nice if we can improve operational efficiency while we do this...
