Public school costs so much because of special education. 15 percent or so of public school children get special education services. They are expensive. Some special cases can be up to 100,000 per year. Catholic schools are able to select their students, so they don't have to have special programs for all their students. Not saying there isn't waste etc. but special education accounts for a bulk of the difference.
I have my doubts that what you say is true.
Let me clarify: I don't doubt that special ed costs a lot; I just doubt that such costs are included in the typical "per pupil" costs we see quoted for public school systems.
And on a different note, I also doubt that even 1% of pubic school kids recieve $100,000 worth of individual services each year. And I bet most of the 15% do not really have special educational needs - rather I bet they fall into the do-gooder-ever-expanding-we-need-more-cash-for-my-special-program-its-for-the-children-after-all-and-if-you-ask-me-50%-of -the-kids-should-be-in-the-program-since-that-would-give-me-job-security-and-a-bigger-budget category.