Why do you think that Bradbury would introduce Clarrise before Montag's wife Mildred ?
In Ray Bradbury's cautionary tale Fahrenheit 451, the author may introduce Clarisse before Montag's wife Mildred because the women are so different—more specifically, their differences are highly supportive of the plot's most central theme: because of technology, people no longer experience life but instead allow society to shape their ideas, behaviors, individualism, self-awareness and so on.
Clarisse McClellan is a young neighbor Montag meets at the book's beginning. She challenges his worldview by asking questions that, in turn, make him ask questions about the direction of his life, his place within society, and even his relationships with others.
Clarisse knows things about the way the world used to be and challenges society's willingness to accept a shadowy existence of that world compared to what it has become.
"There's dew on the grass in the morning."
He suddenly couldn't remember if he'd known this or not. . .
"And if you look"—she nodded at the sky—"there's a man in the moon."
When she asks Montag if he is happy, he thinks it a ridiculous question—one that gains merit as he thinks about it. He recognizes the decline of his marriage and how he and Millie have grown apart. The things Clarisse talks about cause Montag to grasp society's promotion of mindless behavior to eliminate depth in one's thinking and daily living. Books are banned, and independent thinking is discouraged. In these ways, he realizes, members of society are completely under the government's control.
Montag's short association with Clarisse causes him to challenge the status quo of his ideas, career satisfaction, and nearly oblivious existence. In time, he acts out, is chased by the law, and joins the force of rebels living in the woods that are determined to rebuild society in a manner similar to that of years gone by.
Millie is important for different reasons, seemingly because she is the perfect example of someone merely alive, whose brain barely functions, who has no original thoughts, believes and behaves as society wishes, and refuses to question anything. For her, ignorance is bliss. She is society's model citizen, a perfect product of mind control and successful mental programing.
At one point, Montag tries to convey to Millie the powerful experience of watching the old woman living on Elm Street dying for her books. Millie cannot conceptualize such behavior—it makes entirely no sense to her. As Montag questions his part in the disaster (as he sees it) and doubts his ability to continue, Millie demonstrates how very different she is from Clarisse (who actually cares about others):
"You want to give up everything? After all these years of working, because, one night, some woman and her books—"
"You should have seen her, Millie!"
"She's nothing to me; she shouldn't have had books. It was her responsibility, she should have thought of that. I hate her. She's got you going and next thing you know we'll be out, no house, no job, nothing."
Millie's universe is comprised of maintaining things just as they are.
Millie adores their wall-to-wall-TVs. She believes that the people in her daily soap operas (that she watches with her friends) are her real family. She staunchly declares that books are irrelevant—and illegal. She is so distracted from reality by her technology (seashell ear-buds that she listens to all night long and her TV obsessions), that she has no substantial connection to other people—she is barely able to remember Clarisse's accident. Not even death (as seen with the old woman burned inside her own home and the tragic end of young Clarisse) breaks through her zombie-like demeanor.
While Clarisse brings life to Montag's mentally flat world, awakening memories, ideas, and a new desire to think for himself and connect with the world around him, Millie is happiest when she is oblivious. The only thing that seems to get through to her is anything that threatens her uncomplicated and robot-like existence. As society starts to collapse, Mildred leaves Montag; however, she makes sure to report him to the authorities for having books—perhaps her only original thought in the novel.
Bradbury's warnings seem so much more relevant today than when he first wrote his novel. Clarisse exemplifies the person who wishes to experience life to its fullest, searching for self-awareness and expanding her world through knowledge. Millie exemplifies all that is stagnant in a world where people cease to think for themselves. In presenting Clarisse's character first, Bradbury not only provides a glaringly different ideology in contrast to Millie's complacent worldview, it also presents elements of conflict within the plot that will catapult Montag to change, which galvanizes the plot forward.