Selfhood and Autonomy
Uma and Arun are oppressed by their parents in different ways, but both experience an inability to develop as a fully realized human being. They manifest this tension between trying to assert some degree of selfhood and butting up against their parents' domineering and controlling personalities (as well as the patriarchy in Uma's case). Uma in particular does not make much headway with her self-actualization, but Arun's opportunity to study in America and observe the customs of a new family and a new country do help him develop a greater understanding of who he is, where he came from, and what the nuances in his family's relationships mean for him and his sister.
Family
Regardless of the country, family can be, in Desai's view, suffocating and limiting to an individual member's growth and happiness. Parental oppression and neglect are present in both the Patton family and Arun and Uma's family, as are unhappy children.
The Patriarchy
Uma not only suffers from her parents' overbearing nature, but also from the patriarchal society which she inhabits. Her education is considered a waste; she is meant to marry and have children. When she cannot do that, she becomes an embarrassment and an outlier, condemned to stay within her parents' household as a veritable servant. Aruna and Anamika are deleteriously affected as well, with the former struggling to find happiness in her limited role as wife and mother and the latter being subjected to cruelty, abuse, and murder—all carried out by her in-laws and husband with impunity, as her inability to bear children makes her disposable. And Mama, who is by all accounts "happy," is enmeshed in the patriarchal system to the extent that her entire identity is subsumed into Papa's.
Education
Education is opportunity, independence, and growth, which is why Uma so ardently seeks it. She is not a good student, but being at school and learning are joys to her. Arun is more ambivalent about school, but it, and his gender, are his tickets out of India to America. Unfortunately for Uma, education is seen as the purview of boys, as they will be working towards a career. Educating women is considered a waste, and the ideas taught in schools dangerous. Uma's parents' disapproval of Dr. Dutt, an unmarried woman with a career, and the reputation of Mrs. Joshi's daughter, also unmarried and working, is a testament to the general suspicion of educated women.
Colonialism
Though the novel is set in post-Independence India, vestiges of British colonialism are everywhere. There is the convent school, staffed by nuns, and the missionary couple, the O'Henrys, that lives near Uma. Papa extols the merits of English, cricket, and eating meat, lambasting his son for being a vegetarian. He also firmly believes in the value of a foreign degree as opposed to an Indian one, sending Arun abroad rather than letting him stay in India. For upper-middle-class Indians, then, the affiliation with European culture suggests cultural cache; this is a sort of brainwashing holdover from the colonial era, which said there was a hierarchy and European culture is at the top.
Mothers
Both Uma and Melanie need a relationship with their mothers but are essentially neglected by them. In Uma's section, we see her seeking out several mother figures—Mrs. Joshi, Mrs. O'Henry, Mira-masi, and Mother Agnes—all in the hopes of having one of them understand and validate her. Desai suggests that a supportive and loving relationship between mothers and daughters can do a great deal of good, especially for daughters trying to figure out who they are in an intensely patriarchal society.
Religion
Desai does not privilege Hinduism or Christianity in the novel, describing them both as restrictive for women and avoiding suggesting that there is a religious hierarchy (though she alludes to Christianity's negative role in colonizing India). One of the ways she does this is by having Uma, who is Hindu, express interest in both religions for non-doctrinal aspects, such as the convent school's order and rationality and the colorful stories of Hindu gods and goddesses. Uma seeks out religion not for its own sake, but for what it can do to transport her beyond her limited circumstances.