In "Amok Time," it always seemed strange to me that T'Pau didn't mention that the fight was to the death when she was explaining things to Kirk, and that made me wonder if she was intentionally concealing that fact from Kirk. And if she was, I wondered why she would do that. The reasons I can think of:
1. T'Pau doesn't have anything special against Kirk, but she doesn't have anything FOR him, either, and if he dies, that means that no Vulcans die that day, which would probably seem like the best outcome to someone whose job is to manage and look after Vulcans.
2. T'Pau is punishing Spock for bringing "outworlders" to the ceremony -- and possibly for having human friends to begin with -- by killing his friend.
3. T'Pau is punishing Kirk for not being adequately respectful about the whole thing.
4. T'Pau is prejudiced against humans. (Listen to the scorn and loathing in her voice when she pronounces the word "human" when she asks Spock if he's Vulcan or human.
I think #1 is the most probable, but they all seem at least somewhat plausible. And I guess it doesn't have to be either-or; she could tell herself it's #1 while any -- or all -- of the others operates in the background...