It ignores the lack of access to healthy groceries among the urban poor, which is directly due to the "free market." Real grocery stores don't consider it profitable or desirable to open in such areas, so many people are consigned to unhealthy convenience store fare, which leads to nutritional deficiencies, obesity, etc.

Market forces have no built-in consideration of fairness, so if they're allowed to control necessary goods and services, disadvantaged people get screwed. That's inevitable.

Also, it ignores the fact that ~70% of private schools are religious in nature, something which supposed "school choice" advocates definitely have firmly in mind.