We propose that the observed difference in the formation rates of bright low-mass X-ray binaries in metal-rich and metal-poor globular clusters can be explained by taking into account the difference in the stellar structure of main sequence donors with masses between ${\sim}0.85 M_\odot$ and ${\sim}1.25 M_\odot$ at different metallicities. This difference is caused by the absence of an outer convective zone in metal-poor main sequence stars in this mass range. In the result, magnetic braking, a powerful mechanism of orbital shrinkage, does not operate and dynamically formed main sequence – neutron star binaries fail to start mass transfer or appear as bright low-mass X-ray binaries.