What argument is Woolf making about luxury, space and privacy? The following passage will give you a clue: "The inevitable sequel to that visit to Cambridge had started a swarm of questions in my mind, which seemed to demand, unfortunately, a visit to the British Museum. Why did men drink wine and women water? Why was one sex so prosperous and the other so poor? What effect had publicly on fiction? What conditions are necessary for the creation of works of art?"

Woolf knows that many argue that women have not produced great literature to the same extent as men because women are naturally mentally inferior to men. Woolf says that this is not the case at all and contends that men have produced more and greater literature only because they have much more money. More money translates into more leisure time to read, think, and write. More money also means that men can afford to have rooms of their own: in other words, the space and privacy in which to write.
She compares the fine meal at a men's college with the simple, even unpleasant fare at the women's college:

Here was the soup. It was a plain gravy soup. There was nothing to stir the fancy in that. One could have seen through the transparent liquid any pattern that there might have been on the plate itself. But there was no pattern. The plate was plain. Next came beef with its attendant greens and potatoes—a homely trinity, suggesting the rumps of cattle in a muddy market, and sprouts curled and yellowed at the edge, and bargaining and cheapening.

Woolf is saying that because women have to worry so much about money, and have to make do with less, they have a much more difficult time producing great art. Because they cannot depend on having the luxuries of space or privacy, they are at a disadvantage. It is not natural inferiority that holds women back, but the lack of access to the resources men have.