The matter-antimatter asymmetry problem, corresponding to the virtual nonexistence of antimatter in the universe, is one of the greatest mysteries of cosmology. Within the framework of the Generation Model (GM) of particle physics, it is demonstrated that the matter-antimatter asymmetry problem may be understood in terms of the composite leptons and quarks of the GM. It is concluded that there is essentially no matter-antimatter asymmetry in the present universe and that the observed hydrogen-antihydrogen asymmetry may be understood in terms of statistical fluctuations associated with the complex many-body processes involved in the formation of either a hydrogen atom or an antihydrogen atom.