Teaching young people about "privacy" has serious defects if the goal is to promote children's online safety. This commentary points out some the key problems to programs and educational modules with this privacy orientation. Privacy is an abstract and complicated concept, whose norms are in flux, making it difficult to impart clear, relevant, consensus-based messages. We also know very little about how privacy concepts develop in childhood and at what age and in what sequence, making it hard to know what to teach and when. Privacy skills are not necessarily the most important ones for preventing most online harms, including the most serious ones, casting doubt on whether they should receive priority over other prevention skills. Research has also not clearly established connections between many privacy practices and reductions in harm. Most privacy messaging has not been evaluated for how well it is learned, applied and what forms of safety it enhances. As an alternative, the promotion of online safety is best organized, not around privacy, but around the specific harms that educators and children themselves are trying to prevent. The highest priority of these are sexual exploitation, peer bullying and harassment. Such educational safety programs are best built from the foundation of evidence-based programs related to parallel offline dangers.