"There will always be those who mean to do us harm. To stop them, we risk awakening the same evil within ourselves. Our first instinct is to seek revenge when those we love are taken from us. But that’s not who we are.”
~Jim Kirk, Star Trek Into Darkness
I think about this line more than I probably should. Because his statement about the desire to seek revenge might be true of him (just look at the way he lashes out at Khan after Pike’s death), it’s certainly true of both Spock and Uhura (“go get him”), but it’s so inescapably untrue of McCoy.
When he sees Jim’s body, he doesn’t particularly care about getting revenge against Khan; there’s no anger or wrath in his response, only total, utter despair. And what brings him out of that, what brings the life back to his eyes isn’t the thought of revenge, it’s the realization that it might not be too late to save Jim. Bones’ first instinct is to heal—if he can’t do that, for all his temper, he doesn’t see much point in doing further harm.