Cycling tissues such as the intestinal epithelium, germ line, and hair follicles, require a constant flux of differentiated cells. These tissues are maintained by a population of stem cells, which generate differentiated progenies and self-renew. Asymmetric division of each stem cell into one stem cell and one differentiated cell can accomplish both tasks. However, in mammalian cycling tissues, some stem cells divide symmetrically into two differentiated cells and are replaced by a neighbor that divides symmetrically into two stem cells. Besides this heterogeneity in fate (population asymmetry), stem cells also exhibit heterogenous proliferation-rates; in the long run, however, all stem cells proliferate at the same average rate (equipotency). We construct and simulate a mathematical model based on these experimental observations. We show that the complex steady-state dynamics of population-asymmetric stem cells reduces the rate of replicative aging of the tissue-potentially lowering the incidence of somatic mutations and genetics diseases such as cancer. Essentially, slow-dividing stem cells proliferate and purge the population of the fast-dividing - older - cells which had undertaken the majority of the tissue-generation burden. As the number of slow-dividing cells grows, their cycling-rate increases, eventually turning them into fast-dividers, which are themselves replaced by newly emerging slow-dividers. Going beyond current experiments, we propose a mechanism for equipotency that can potentially halve the rate of replicative aging. Our results highlight the importance of a population-level understanding of stem cells, and may explain the prevalence of population asymmetry in a wide variety of cycling tissues.