Why was it so important for Rukmani to have a son in "Nectar in a Sieve"?
In Indian culture, gender roles were strictly prescribed, especially in rural areas during the mid-1900s when the story took place. A woman's role was to take care of the house, raise the children, cook, and oversee religious and cultural rites. A man's role was to earn money to support the family. Couples were expected to have children, and faced great stigma if they, for whatever reason, did not. It was especially important for a woman to have sons because a son could be taught his father's trade and eventually assume responsibility for the family's financial well-being. Daughters, on the other hand, were a double financial liability - traditionally, they could not earn money on their own, yet they would require a dowry from the family in order to eventually marry.
These standards still apply in many parts of India today.
In Indian cultures it's is very important that you bear children. And when you do you have to have an dowery for them if they are girls. In Ruku's situation it was important for her to bear boys because she didnt marry a rich husband and one girl was enough considering that she had one already, and wasnt rich enough to have dowery money for many girls.
Indian society was and is still patriarchal. Daughters are always considered to be a liability because the parents have to pay a 'dowry' (bride price) to get her married; whereas a son is the one who brings home the dowry.
The daughter stays at home looking after the household while the son works to increase the family income.
Most importantly, only the son and that too the eldest son can light the funeral pyre of his parents or his siblings.