We investigate the magnetization reversal of individual Co islands on Cu(111) in the size range of N=700 to 18000 atoms by spin-polarized scanning tunneling microscopy at 8 K. The switching field H_sw changes with island size in a nonmonotonic manner: it increases with island size and reaches a maximum value of 2.4 T at N=5500 atoms, and it decreases for larger islands. We extract the energy barrier for magnetization reversal as a function of island size. The maximum H_sw corresponds to an energy barrier of 1 eV. Our results elucidate a crossover of the magnetization reversal from an exchange-spring behavior to domain wall formation with increasing size at around 7500 atoms.