Does private high school count as a deductible expense against 10% early withdrawal from IRA, or does it have to be college or university? What is the exact requirement

Sorry, no.

The 10% early distribution exemption from an IRA is only for qualified higher education expenses at an eligible educational institution.

An eligible educational institution is a school offering higher education beyond high school. It is any college, university, trade school, or other post secondary educational institution eligible to participate in a student aid program run by the U.S. Department of Education.

Got it, thanks!