1. In 1997 West, Brown & Enquist published a theoretical explanation for the long-known empirical observation of 3/4-power scaling of organismal metabolic rates with body mass, using an attractive combination of general physical and physiological principles with evolutionary optimization. This model generated hundreds of studies, exploring its implications for physiology, populations, biodiversity, whole-ecosystem functioning, and even medical, engineering and social sciences. 2. However, the evolutionary optimization part of the model has never been carefully scrutinized. 3. In this article we perform the evolutionary optimization as proposed by the authors rigorously and show that it actually leads to a biologically irrelevant network, i.e. a single vessel. 4. Moreover, we find that by relaxing some assumptions in a realistic way we obtain a feasible network but with isometric scaling of metabolism, which is in conflict with Kleiber's empirical law of an allometric exponent of around 3/4. 5. Hence, we conclude that the West-Brown-Enquist model cannot account for the observed universal metabolic scaling relation. 6. As possible solutions to this paradox, we discuss (weak) body-size dependence of capillary properties (leading to different predictions of intra-and inter-specific metabolic scaling), and expanding the West-Brown-Enquist model to an integrated network model (including body shape and oxygen transport to and from the arterial system). Alternatively, the ultimate explanation for the observed allometric patterns may need to be found outside the framework of flow-limited network theory. 7. We conclude that Kleiber's law is still as theoretically unexplained as ecologically important.