This could be a good theme for the sequel. NuSpock sees himself as an expert on command. He has command experience and is the creator of one of the Academy’s key tests of command ability. NuKirk is inexperienced and has little regard for what the Academy teaches about it.
NuSpock could see NuKirk as an on-the-job-trainee and himself as the trainer (which would address Wynterhawk’s question of why NuSpock volunteered to be NuKirk’s first officer). NuKirk has his own ideas and is not receptive to what NuSpock is trying to teach.