One of Woolf's arguments in A Room of One's Own is that if women had a tradition of female writers behind them to inspire them, as men do with male writers, and also the broad access to writing that men do, they would have an easier time becoming great writers. At the end of the essay, she mentions the connection between reading and writing when she states:
I thought of the organ booming in the chapel and of the shut doors of the library . . . and, thinking of the safety and prosperity of the one sex and of the poverty and insecurity of the other and of the effect of tradition and of the lack of tradition upon the mind of a writer, I thought at last that it was time to roll up the crumpled skin of the day.
When Woolf thinks of the library, she is remembering how she was barred from entering a prestigious university library that held a Thackeray manuscript solely because she was a woman. Without this access to reading material, such as manuscripts, it is harder for women to study how writers work. Without the wealth and resources men have to read in leisure, women have a harder time writing.
Woolf also writes:
But lay the blame where one will, on whom one will, the illusion which inspired Tennyson and Christina Rossetti to sing so passionately about the coming of their loves is far rarer now than then. One has only to read, to look, to listen, to remember.
The context for the quote above is World War I. Woolf is saying that before World War I, people were more willing to read love poetry because they were able to maintain their romantic illusions. The brutality of the war ripped that romantic veil away, so that people were no longer interesting in reading or writing about false happiness. In this case, reading and writing are both seen as a response to the cultural circumstances in which people live. This highlights Woolf's argument that women's lesser production of great literature is a result of cultural forces, not the innate inferiority of women.
It is good to keep in mind that Woolf's method in this essay is meandering, using description to build her case that women have fewer opportunities than men.