1. Growth in body size is accompanied by changes in foraging capacity and metabolic costs, which lead to changes in competitive ability during ontogeny. The resulting size-dependent competitive asymmetry influences population dynamics and community structure, but it is not clear whether natural selection leads to asymmetry in intraspecific competition. 2. We address this question by using a size-structured consumer-resource model, in which the strength and direction of competitive asymmetry between different consumer individuals depends on the scaling of maximum ingestion and maintenance metabolism with consumer body size. We use adaptive dynamics to study selection on the scaling exponents of these processes. 3. Selection leads to an identical scaling of maximum ingestion and maintenance metabolism with consumer body size. Equal scaling exponents neutralise strong competitive differences within the consumer population, because all consumer individuals require the same amount of resources to cover maintenance requirements. Furthermore, the scaling exponents respond adaptively to changes in mortality such that biomass production through growth or reproduction increases in the life stage that is subject to increased mortality. Also, decreasing size at birth leads to increased investment in juvenile growth, while increasing maximum size leads to increased investment in post-maturation growth and reproduction. 4. These results provide an explanation for observed variation in the ontogenetic scaling of metabolic rate with body size. Data of teleost fish are presented that support these predictions. However, selection towards equal scaling exponents is contradicted by empirical findings, which suggests that additional ecological complexity beyond this basic consumer-resource interaction is required to understand the evolution of size-dependent asymmetry in intraspecific competition.