How we cite our quotes: All quotations are from Star Trek II: The Wrath of Khan.
Quote #1
SAAVIK: I don't believe this was a fair test of my command abilities.
KIRK: And why not?
SAAVIK: Because...there was no way to win.
KIRK: A no-win situation is a possibility every commander may face. Has that never occurred to you?
SAAVIK: No sir. It has not.
Saavik, like Kirk, doesn't like to lose. She's bothered by the notion that there are some scenarios that you just can't win, and the need to find a way around it drives her forward as an officer. It's a tough way to live, but you can see the results in the officer she's becoming.
Quote #2
KIRK: You're bothered by your performance on the Kobayashi Maru.
SAAVIK: I failed to resolve the situation.
KIRK: There is no correct resolution. It's a test of character.
SAAVIK: May I ask how you dealt with the test?
KIRK: You may ask. That's a little joke.
Saavik isn't strictly competing with Kirk here, but she is interested in seeing how he topped the scenario she couldn't, perhaps in hopes of finding a way to top it herself.
Quote #3
SPOCK: Really, Doctor McCoy, you must learn to govern your passions. They will be your undoing. Logic suggests...
McCOY: Logic? My God! The man's talking about logic! We're talking about universal Armageddon! You green-blooded, inhuman...
The joke goes that Spock is the passionless superego and McCoy is the rampaging id, both competing to have the final word of advice for their buddy Kirk. That competition helped define the original series.