It's phoney emotionalism. The only reason it works is because people play back the scene from Khan in their heads. It doesn't stand on its own, nor does it suit a story of two glorified cadets who have barely really gotten to bond.
Oh come on. Putting aside Kirk, who for all we know had a college degree under his belt and came to the Academy basically as an OCS prospect, Spock is far from a glorified cadet. He was already at least a Lt. Commander by the middle of the 1st movie.