In episode 3.11 Final Exam, both Chuck and Sarah are facing a Kobayashi Maru. Hence the tragedy of their situation and the sense of hopelessness they both feel. Along with the ending of 3.08 Fake Name (the Ordeal stage of the Hero’s Journey), this is the absolute nadir of their relationship. Sarah’s Kobayashi Maru is that, no matter what she does, she’s going to lose Chuck and herself. She doesn’t want to proctor Chuck’s red test because she doesn’t want him to become a cold-blooded assassin.
But if she doesn’t proctor it, Chuck might not pull the trigger and could be killed by the mole. If she proctors it, she would never forgive herself but it might save Chuck’s life since she’s the only one that can convince Chuck to pull the trigger.
She’s trapped by her feelings for him into using his feelings for her against him in order to save him, even though doing so kills her. So, she decides to sacrifice herself to save him. You can see all hope leave her face as she leaves the table, and she’s engulfed in her own guilt for having encouraged him into the spy life.
Chuck’s Kobayashi Maru is that, no matter what he does, he’s going to lose Sarah or himself. If he doesn’t execute the mole, he won’t be a spy and will lose Sarah. If he does it, he’ll be a spy and possibly be with Sarah (or not; he doesn’t know it yet) but at the cost of his moral principles.
[Of course, there’s always the option to not execute the mole and run away together but that may be a long shot at this point—Sarah doesn’t offer herself as the prize for Chuck giving up on the spy life because she tried that in Prague. She made herself vulnerable and failed and was devastated. She isn’t going to make that mistake again.]
So Sarah takes herself out of the equation for Chuck by not making Chuck’s choice about her. She frames it as “what kind of person do you want to be? The old Chuck?” (And there’s nothing wrong with that, in her eyes.) “Or spy Chuck, which is what you’ve been working toward?”
To Chuck, being his old self is a no-no. He doesn’t see his old self as Sarah does—innocent, charming, and heroic. He sees his old self as a neurotic loser. But he doesn’t want to become a cold-blooded assassin either.
Hence, the final exam on the kind of person he wants to be, a final choice between his moral principles and his ambitions, the hour upon which the whole third season hinges and that it was hinted at since the very first scene in 3.01 Pink Slip, when Chuck refused to fake-kill Yuri during the Prague simulation.
Incidentally, some have speculated that this red test is Shaw’s idea of testing Chuck’s and Sarah’s ultimate allegiance to the CIA after their decision in 3.10 Tic Tac to commit treason in order to help Casey. And also his final piece to break up Chuck and Sarah so that he can have Sarah for himself. If so (“No Burbank, no baggage,”), it is cunning genius—use Chuck’s and Sarah’s feelings for each other against each other to achieve his purpose and keep his hands clean.