In answering this question, it is important to understand the meaning of "rhetoric." While there are many applications for the word, the one that I find most relevant is...
...the ability to use language effectively.
While this is a general definition, Clarisse's manner of seeing and sharing what she sees with those around her—specifically Montag—has a compelling effect in Bradbury's Fahrenheit 451.
Clarisse's diction is concise—in a world where people question nothing, Clarisse is a refreshing (Montag learns) and unusual person. While their society promotes unthinking behavior, Clarisse questions everything.
Clarisse notes that Montag is a fireman—which she could tell with her eyes closed; he understands that she is referring to the smell of kerosene on his clothes. He says that it is like perfume to him. The ludicrousness of this statement is apparent in her query:
Does it seem like that, really?
Montag is startled by her questions, asking her at one point if she has no respect—a defense mechanism where he tries to use his job of burning books to intimidate the young woman because he doesn't know how to respond to her unusually direct conversation.
When Montag asks why she is out so late and how old she is, she is particularly direct in her response, a manner markedly different than the way those around Montag speak:
I'm seventeen and I'm crazy. My uncle says the two always go together.
As they continue, she shares a truth that Montag obviously has never considered before:
You know, I'm not afraid of you at all.
He wonders—with surprise—why she would say such a thing. She replies that so many people are afraid of firemen.
Clarisse has not yet learned the art of guile, it would seem. When she asks him if he's ever actually read one of the books he burns, he laughs and reminds her that it's against the law. She responds, "Oh. Of course." We can infer by her response that she almost needs to be reminded of this fact, pointing to the unusual family of which she is a part—people that stay up all night not distracted by the contraptions of society (like the ear shells or parlor walls), but actually talking and engaging in original thought—ideas not dictated and controlled by the government.
Clarisse's direct way of speaking is strange and confusing for Montag; at the same time the author uses Clarisse to enlighten Montag:
You laugh when I haven't been funny and you answer right off. You never stop to think what I've asked you.
When society tells one how to respond and how to feel, thinking is not generally required. Montag is not even aware that he fails to think.
Clarisse tells Montag that she has a lot of time to think about things; he responds, uneasily, that she thinks of too many things.
Then she shares observations with him at a rapid fire pace that leave Montag stunned and irritated.
"Did you know that once billboards were only twenty feet long? But cars started rushing by so quickly they had to stretch the advertising out so it would last."
"I didn't know that!" Montag laughed abruptly.
"Bet I know something else you don't. There's dew on the grass in the morning.
And if you look...there's a man in the moon.
When Montag asks about her family that is actually home and having a discussion, Clarisse says:
My uncle was arrested another time—did I tell you?—for being a pedestrian.
Montag is in awe that the family talks because he cannot imagine what there is to talk about. In his home, Mildred watches parlor walls and listens to the ear shells. They don't have conversations.
Before she says goodnight, Clarisse asks Montag something that really trips him up—for no one else ever asks:
Are you happy?
In this tale where original thought and freedom of expression are strictly guarded, controlled and discouraged by the government, Clarisse's ease in sharing her ideas is unexpected by Montag and deeply unsettling.
Bradbury uses Clarisse's manner of speech to introduce the concept of social dissonance and dysfunction that has almost completely overwhelmed this futuristic society—a concern the author had that seems all too justified today. Amid the rhetoric of our modern-day society, in politics, journalism and even how people relate to one another in society at large, it would seem Bradbury had something concrete about which to be anxious.
Clarisse's voice is the one that catches Montag's attention and places him on the road to discover what has been lost and almost destroyed in the government controlled burning of books and mind numbing of the masses. In a society here the intellectual rights of the individual have been suppressed, Clarisse's rhetoric provides the setting for Montag's eventual awakening and desire to carry on the contemplation and challenge of societal norms that Clarisse's character first introduces into the novel.