No, tuition and related expenses paid to attend a private high school do not qualify for an education credit. According to the retrieved information, an eligible educational institution for the purposes of education credits, such as the American Opportunity Tax Credit (AOTC) and the Lifetime Learning Credit (LLC), must be a postsecondary institution. This includes colleges, universities, vocational schools, or other postsecondary educational institutions that are accredited and eligible to participate in federal financial student aid programs administered by the Department of Education. High schools, including private high schools, do not meet this definition and therefore do not qualify as eligible educational institutions for these education credits.
Sources:
Publication 970 (2023)
Notice 97-73, 1997-51 IRB 1
§ 25A. American Opportunity and Lifetime Learning credits