Differences in Public Education Curriculum vs. Private
One of the key differences between public and private educations is how they are funded. The sources of these dollars hold some power over the institutions they donate to, and this can heavily affect how the schools operate and teach.
For public schools, their money primarily comes from federal and state funding. This gives the government a large amount of control over the curriculum of public schools. Department of Education standards and policies are able to reach many of the nation's schools through this control. In a system with this level of central control, as well as this spread out across the nation, it makes creating impactful change in curriculum via philanthropy hard to do. To create a difference in the world of modern education, an organization cannot simply give money and ask for changes to be made. One must spend their money lobbying the government for certain policies and funding the creation of separate bodies of control over educational systems such as charter schools.
For private schools, money comes from donations and tuition, as well as from other avenues. This leads to many more points of control for donors to influence. It's much more realistic for a donor to exert some level of control over a private school regarding certain policies than for a public school. This influence leads to the creation of certain quirks in curriculum such as specific required courses or strange graduation requirements.