Among carnivorous plants, Darwin was particularly fascinated by the speed and sensitivity of snap-traps in Dionaea and Aldrovanda. Recent molecular work confirms Darwin's conjecture that these monotypic taxa are sister to Drosera, meaning that snap-traps evolved from a ‘flypaper’ trap. Transitions include tentacles being modified into trigger hairs and marginal ‘teeth’, the loss of sticky tentacles, depressed digestive glands, and rapid leaf movement. Pre-adaptations are known for all these traits in Drosera yet snap-traps only evolved once. We hypothesize that selection to catch and retain large insects favored the evolution of elongate leaves and snap-tentacles in Drosera and snap-traps. Although sticky traps efficiently capture small prey, they allow larger prey to escape and may lose nutrients. Dionaea's snap-trap efficiently captures and processes larger prey providing higher, but variable, rewards. We develop a size-selective model and parametrize it with field data to demonstrate how selection to capture larger prey strongly favors snap-traps. As prey become larger, they also become rarer and gain the power to rip leaves, causing returns to larger snap-traps to plateau. We propose testing these hypotheses with specific field data and Darwin-like experiments. The complexity of snap-traps, competition with pitfall traps, and their association with ephemeral habitats all help to explain why this curious adaptation only evolved once.