Private groups could develop and maintain educational standards and the means of measuring them, in much the same way as industrial groups have developed standards for their industries. Privatizing education in this way could also answer the problem of heavy-handed bureaucracy and excessive administrative costs, which are about two times higher in the U.S. than in other wealthy countries. Students cannot know everything, so we must be selective in setting forth educational goals. Once again, this is difficult to do in the U.S., because educators, parents, and students differ substantially in their preferences about what to learn and how to learn it. Again, diversity of approaches is in order.
Markets also respond to the lack of incentives for improvement.
In a privatized system of education, providers who were unable to attract customers would go out of business. In fact, we trust parents to make choices for their children all the time, in every imaginable arena, except in education. In all but the smallest minority of cases, parents care more about their children than anyone else can. I'm much more comfortable trusting parents to make education decisions for their children than trusting bureaucrats and government officials. I suspect that many of your readers may even believe that their children may be the first generation that learns less than their parents did.