An annotated synthesis of textbook definitions of parasitism is presented. Most definitions declare parasitism is a long-lasting relationship between individuals of different species harming the hosts. The infection-induced costs are interpreted as diseases in the medical-veterinary literature. Alternatively, evolutionary ecologists interpret it as a reduction of host's fitness (longevity, fertility or both). Authors often assume that such effects decrease host population growth and select for antiparasitic defences, which is not necessarily true because infections may simultaneously express opposite effects at different levels of biological organization. (i) At the cellular level, infection-induced cell growth, longevity and multiplication may yield tumours maladaptive at higher levels. (ii) At the individual level, reduced host longevity, fertility or both are interpreted as disease symptoms or reduced fitness. (iii) Contrary to common sense, the growth rate of infected host lineages may increase in parallel with the individuals' reduced survival and fertility. This is because selection favours not only the production of more offspring but also their faster production. (iv) Finally, infections that reduce host individuals' or lineages' fitness may still increase infected host populations' growth rate in the context of ecological competition. Therefore, differences between parasitism and mutualism may depend on which level of organization one focuses on.