There are many private universities and if trying to compare the words public and private, they are different UK to US in education entities.
To consider only state government funded schools as main source of funding, each state decides on its structure of taxes and how that money gets spent. Public schools may get some Federal level support, but their main operation funds are at individual state level.
If a state has high tax rates, people can move to a different state.
The money collected has to be divided among state services.
What's more, each state college or university has one lower cost for in-state students and a higher cost for students from other states or out of the USA entirely.
Even with in-state tuition, it varies.
A college education in the USA is not considered a human right.
Further, there are technical schools devoted to teaching trades such as plumbing or electrician.
Public education is free for 13 years, Kindergarten through 12th grade.
It is in the tax rates and skew of wealth, where the USA is highly capitalistic, and I believe it is failing now because of it. Total taxes in the USA are lower than other industrial countries, and still people complain.
There is also the issue that the health care industry is 18% of Gross Domestic Product putting a large burden and another 4% for military and homeland security. They are a huge burden unlike other countries, as two other broken institutions.