When Clare first meets Henry as a six-year-old, she's a good Catholic schoolgirl, who believes in God and good manners (aside from stepping on her brother's toes, maybe). She's very suspicious of Henry and not easily convinced by his stories of time traveling. Her worldview appears to be very traditional and very secure.
But the more time Clare spends with Henry, the more she trusts him and longs for his company. It's not until her teen years that she realizes that she's the only girl with "a Henry" and, more importantly, that her relationship with him makes her rather different from her peers. He challenges her secure God-created world with the sheer reality of his presence. Her growing attraction to him, a grown 43-year-old man, leaves her disinterested in boys her age.
Of course, her peers make fun of her for being different. Especially in her teens, she's known as "Miss-Look-But-Don't-Touch." Clare humors the humiliating treatment, for the most part, because she loves spending time with Henry and she knows she will be with him in her future. It is that certainty, the idea that her future is already determined, that she both clings to and rejects throughout her relationship with Henry. When Gomez repeatedly urges her to not marry Henry, she tells him, "I have no choice… I've seen my future; I can't change it, and I wouldn't if I could" (1.8.203). She reiterates that statement many times throughout the novel, because she wants to believe that having no choice means making no mistakes: "I never chose Henry. He never chose me. So how could it be a mistake?" (1.8.217).
Despite the comfort it sometimes provides, the idea that her relationship with Henry was pre-determined also occasionally infuriates her. She feels patronized by Henry when he tells her "what she likes," before she has even realized these preferences herself. She asks to go house-hunting by herself because she doesn't want to be influenced by Henry's knowledge of their future house – she wants to pick it out on her own. Sometimes she completely disappears into her work, which Henry believes to be her way of escaping the determinism that pervades their life.
Her inability to have children with Henry, however, seems to be the last straw in her frustration with this determinism. She refuses to go along with Henry's belief that nature doesn't want them to have a child because Henry is a faulty organism. Although Henry tells her that he's never seen them with a child in their future, she challenges this verdict, again and again, and her faith finally prevails. She gives birth to Alba, proving Henry's omniscience wrong.
Although Clare left her family home to lead a life rather different from the way she grew up, her family continues to play a vital role in her life. When Clare brings Henry home to meet her family, she's very concerned that everyone make a good impression. She's eager to please her parents, especially her mother. At the same time, Clare really dislikes the fake happy family appearance that they put on for Henry and feels embarrassed by her mother's inappropriate behavior. She seems to struggle with uniting her new independent self and with her old traditional self.
But lying beneath Clare's difficulty combining elements of her past and her present, she struggles with the fact that, much like Henry, she never really had a mother. Clare was raised by Etta, the housekeeper, while her own mother hovered somewhere "off in the clouds." After her mother's death, Clare is devastated, because she never even had a chance to have a heart-to-heart with her mother. When she later discovers that her mother dedicated a poem to her that not only witnesses her love but also her respect for Clare's choices in life, she's finally able to let go of the quest for acceptance that plagued her since childhood.
Much like Audrey Niffenegger herself, Clare is a papermaking artist, very committed to her craft. She loves papermaking because she loves tangible things. "I like to do things directly, touch the textures, see the colors" (2.1.75). Touching things is what makes them real to her. Then why does she fall in love with Henry, a time traveler, the most elusive person of all? A case of opposites attract?
On the other hand, though, Clare's work as an artist centers around birds. Birds seem to stand for the opposite of tangible – for the fleeting, for the Henry that disappears. On their first date in the present, Clare explains to Henry that she makes birds because they represent "longing" (1.1.59). The first time the feeling of longing enters Clare's life is when she waits for Henry. She thinks of him as an "angel," an ever-elusive bird. So it's not really a stretch to argue that her love of making birds grew out of her relationship with Henry. He becomes and continues to be her artistic muse.
When Henry loses his feet, the wings of his universe, Clare sculpts new wings for him. Giant and painted blood red, they reflect the change Henry has undergone while in her universe. She now thinks of him as a "terrifying angel." He is still the bird Clare longs for, and hopes to be with. But she also recognizes the pain their relationship has brought to her life, because it's been a life of longing to touch the intangible.