Perhaps the main theme of Fasting, Feasting by Anita Desai is the operation of patriarchy on the lives of Indian women, with emphasis on how it limits their opportunities for happiness and self-development, and traps them in marriages that are almost a form of slavery.
Anamika's narrative line is perhaps the most chilling condemnation of arranged marriage in the book. Intelligent enough to win a scholarship to Oxford, instead she is married off and maltreated, and perhaps even killed by her husband. The protagonist, Uma, also deeply wishes for education and independence, and also ends up in a bad marriage, but manages to escape that; however, she still ends up in her parents' home as a middle-aged woman, acting as a sort of servant to her father and mother.
In the section set in the United States, the Patton family is portrayed as equally dysfunctional, with patriarchy, again, as the main culprit.
Thus the main themes of the novel are patriarchy, family, and education, with women's education in particular and women's spirituality acting as loci of resistance to patriarchy.