The details of this conversation about a poem Tweedledee has just recited suggest that Alice knows this poem and has heard it recited before. Alice cannot use reason to win an argument in the mirror world. Alice does not really understand what the poem is about. Alice wants to hear the poem again before moving along.

I looked this question up and found the passage it is about. It is the following:

Read this excerpt from Through the Looking-Glass by Lewis Carroll.

"I like the Walrus best," said Alice: "because you see he was a LITTLE sorry for the poor oysters."

"He ate more than the Carpenter, though," said Tweedledee. "You see he held his handkerchief in front, so that the Carpenter couldn't count how many he took: contrariwise."

"That was mean!" Alice said indignantly. "Then I like the Carpenter best—if he didn't eat so many as the Walrus."

"But he ate as many as he could get," said Tweedledum.

This was a puzzler. After a pause, Alice began, "Well! They were BOTH very unpleasant characters—"

The details of the conversation suggest that:

B. Alice cannot use reason to win an argument int he mirror world.

Explanation:

No matter what reason Alice gives to choose a character as her favorite from the poem she just heard, Tweedledee and Tweedledum will refute it. Even though her logic is not incorrect, neither is theirs. Therefore, logic and reasoning are not enough for Alice to win an argument in this world. She may very well say something completely biased, choosing a character simply for the sake of choosing. Then, they will not be able to argue with her. But, offering explanations based on logic will always be a problem, since they will be able to offer a counterargument.