Nitrogen reduction reaction (N2RR) carried out on biomimetic catalytic systems is considered to be a promising alternative for the traditional Haber-Bosch ammonia synthesis. Unfortunately, the selectivity of the currently known biomimetic catalysts is poor, as they also catalyze the unproductive hydrogen evolution reaction (HER). In the present computational study, we examine the HER activity of early N2RR intermediates in EP3 (E = B, Si) ligated single-site biomimetic iron complexes by calculating and comparing the activation Gibbs free energies of HER and N2RR elementary steps. We find that, in contrast to previous suggestions, early N2RR intermediates are not likely sources of HER under turnover conditions, as the barriers of the competing N2RR steps are significantly lower. Consequently, future research should focus on preventing other potential HER mechanisms, e.g., hydride formation, rather than accelerating the consumption of early N2RR intermediates as proposed earlier to design more efficient biomimetic catalysts.