Evolutionary psychiatrists often consider schizophrenia to be an enigma: how come natural selection has not yet eliminated the so-called `schizophrenia genes´ if the disorder is fairly common, heritable and harmful for the reproductive success of its carriers? Usually, the answer is that the schizophrenic genotype is subject to some kind of balancing selection: the benefits it confers would then outbalance the obvious damage it does. However, in this paper I will show that the assumptions underlying such resolution are at least implausible, and sometimes even erroneous. First of all, I will examine some factual assumptions, in particular about schizophrenia`s impact on reproductive success, its genetics, its history, and its epidemiology. Secondly, I will take a critical look at a major philosophical assumption in evolutionary psychiatric explanations of schizophrenia. Indeed, evolutionary psychiatrists take it for granted that schizophrenia is a natural kind, i.e. a bounded and objectively real entity with discrete biological causes. My refutation of this natural kind view suggests that schizophrenia is in fact a reified umbrella concept, constructed by psychiatry to cover a heterogeneous group of disorders. Therefore, schizophrenia, as we now know it, simply does not have an evolutionary history.