arXiv:2509.26474v1 Announce Type: new Abstract: Machine learning in medicine is typically optimized for population averages. This frequency weighted training privileges common presentations and marginalizes rare yet clinically critical cases, a bias we call the average patient fallacy. In mixture models, gradients from rare cases are suppressed by prevalence, creating a direct conflict with precision medicine. Clinical vignettes in oncology, cardiology, and ophthalmology show how this yields missed rare responders, delayed recognition of atypical emergencies, and underperformance on vision-threatening variants. We propose operational fixes: Rare Case Performance Gap, Rare Case Calibration Error, a prevalence utility definition of rarity, and clinically weighted objectives that surface ethical priorities. Weight selection should follow structured deliberation. AI in medicine must detect exceptional cases because of their significance.