Quote 1
"He's dreaming now," said Tweedledee: "and what do you think he's dreaming about?"
Alice said "Nobody can guess that."
"Why, about you!" Tweedledee exclaimed, clapping his hands triumphantly. "And if he left off dreaming about you, where do you suppose you'd be?"
"Where I am now, of course," said Alice.
"Not you!" Tweedledee retorted contemptuously. "You'd be nowhere. Why, you're only a sort of thing in his dream!"
"If that there King was to wake," added Tweedledum, "you'd go out – bang! – just like a candle!" (Looking-Glass 4.37-42)
Alice has been assuming that the entire Looking-Glass World is something she owns, a fantasy that she came up with. Now she's faced with the possibility that she is only a character in someone else's fantasy, and she doesn't really like the idea.
Quote 2
"We must have a bit of a fight, but I don't care about going on long," said Tweedledum. "What's the time now?"
Tweedledee looked at his watch, and said "Half-past four."
"Let's fight till six, and then have dinner," said Tweedledum. (Looking-Glass 4.74-76)
Fighting, both verbal and physical, are assumed to be inextricable parts of life. Ridiculously, Tweedledum and Tweedledee schedule their fight so that they can fit it in before a meal. It doesn't seem to occur to them that they could not fight.