The human hair cycle is a complex, dynamic organ-transformation process during which the hair follicle repetitively progresses from a growth phase (anagen) to a rapid apoptosis-driven involution (catagen) and finally a relative quiescent phase (telogen) before returning to anagen. At present no theory satisfactorily explains the origin of the hair cycle rhythm. Based on experimental evidence we propose a prototypic model that focuses on the dynamics of hair matrix keratinocytes. We argue that a plausible feedback-control structure between two key compartments (matrix keratinocytes and dermal papilla) leads to dynamic instabilities in the population dynamics resulting in rhythmic hair growth. The underlying oscillation consists of an autonomous switching between two quasi-steady states. Additional features of the model, namely bistability and excitability, lead to new hypotheses about the impact of interventions on hair growth. We show how in silico testing may facilitate testing of candidate hair growth modulatory agents in human HF organ culture or in clinical trials.