Over the past 50 million years, successive clades of large carnivorous mammals diversified and then declined to extinction. In most instances, the cause of the decline remains a puzzle. Here we argue that energetic constraints and pervasive selection for larger size (Cope's rule) in carnivores lead to dietary specialization (hypercarnivory) and increased vulnerability to extinction. In two major clades of extinct North American canids, the evolution of large size was associated with a dietary shift to hypercarnivory and a decline in species durations. Thus, selection for attributes that promoted individual success resulted in progressive evolutionary failure of their clades.