The hierarchy of social organization is a ubiquitous property of animal and human groups, linked to resource allocation, collective decisions, individual health, and even to social instability. Experimental evidence shows that both the intrinsic abilities of individuals and social reinforcement processes impact hierarchies; existing mathematical models, however, focus on the latter. Here, we develop a rigorous model that incorporates both features and explore their synergistic effect on stability and the structure of hierarchy. For pairwise interactions, we show that there is a trade-off between relationship stability and having the most talented individuals in the highest ranks. Extending this to open societies, where individuals enter and leave the population, we show that important societal effects arise from the interaction between talent and social processes: (i) Despite a positive global correlation between talent and rank, paradoxically, local correlation is negative, and (ii) the removal of an individual can induce a series of rank reversals. We show that the mechanism underlying the latter is the removal of an older individual of limited talent, who nonetheless was able to suppress the rise of younger, more talented individuals.