Clarisse specifically states,
"I'm afraid of children my own age. I'm afraid of them and they don't like me because I'm afraid."
Here is the deal with Clarisse. She represents everything that is real. This world that Fahrenheit 451 takes place in contains nothing of the reality that we want to have in place today... except Clarisse. She fears her peers because the are reckless and they don't have any sense of responsibility.
Just a few paragraphs later Clarisse claims that she really enjoys watching people. She doesn't necessarily know them, but she likes to use her imagination and try to figure out where people are going and what they intend to do when they get there.
These features of Clarisse prove that she thinks much more than the average kid in the society represented by this novel.
During a conversation with Montag (in Part One), Clarisse admits to being afraid of her peers:
I'm afraid of children my own age. They kill each other…I'm afraid of them and they don't like me because I'm afraid.
This quote is important because it creates a contrast between Clarisse and her peers. They thrive on the dangerous forms of entertainment which were introduced into their society after books were made illegal. Clarisse, on the other hand, dislikes such pursuits: she would much prefer to "watch people" or ride the subway all day than joyride or go the Fun Park. Clarisse is, therefore, a social outcast, and it is this difference that inspires her fear of her peers.
It is ironic, then, that Clarisse is killed by a group of her peers who are out joyriding, one of the activities to which she is so opposed. Montag comes to realize this fact in Part Three when he is fleeing the Mechanical Hound, and through this experience he realizes just how scary groups of teenagers can be.