I think it's apples and oranges. I think Spock was upset about Kirk cheating on the Kobyashi Maru. It does make Kirk upset, but Spock jumps down his throat in that scene, as much as a Vulcan can. He is talking over Kirk and very fast. Not the greatest and most logical thing that Spock has ever done.
However, this was raw. Within hours of losing his mother, Spock is being accused of never loving her. Spock has been bullied and teased for having this "bad bloodline" in the eyes of the Vulcans. He tells the Vulcan science Academy off for say it was a "disadvantage." He beats the crap out of the boy who calls her a whore. This is what he's had to put up with. Remember, he doesn't like Kirk. He's kicked him off the ship, from Spock's perspective, Kirk is just another bully.
I can tell you after losing a parent, if someone had accused me of not loving my father, hours after his death, I would've gotten angry or cried. Say it to me now and it will probably roll off my back because their opinion carries little weight. Kirk has lived his entire life without his father and that is a part of his character, searching for that father figure or some part of his father's legacy. But it's not a fresh wound. He's had time to get used to the fact.