Woolf's line of argument begins with her question about "what state of mind is most propitious for creative work." It involves the hypothetical (made up) sister of Shakespeare, called "Judith" by Woolf, and is part of her examination of the state of mind possessed by Shakespeare who is an undisputed genius. Woolf's line of argument is not exactly a clear one because it is predicated, at least in part, upon her presupposition "that we know nothing about Shakespeare's state of mind" except that his "mind was incandescent, unimpeded" and "expressed completely."
Her line of argument relevant to Shakespeare's sister concludes with the pronouncement that finding a woman of genius in Shakespeare's state of mind would have been an impossibility:
That one would find any woman in that state of mind in the sixteenth century was obviously impossible.
Woolf uses the made-up life of Judith to illustrate some of the reasons that this conclusion is necessary. Some of her points are these. In a working class family, the son may be sent to be educated locally while the daughter will be kept at home to learn domestic work. The son may go off to seek his fortune in a distant town, like Shakespeare sought his in London, while the daughter will be expected to marry early and very often against her wishes. The son may find opportunities opening before him while the daughter will find opportunity only in an escape from coercion. This is where the tragedies begin that lead the male and female down incommensurately oppositional roads. While the son finds opportunities opening before him, the daughter finds opportunities closing in on her leading her, in Woolf's speculations, to the inevitable end of ignobility or death.
Another point in Woolf's argument is that everything in society and custom restricted a woman of genius from exposing or developing her talents as Shakespeare was permitted to develop his. A strong support for this point is the opinions on women expressed by male writers in different periods. One of particular note, because it was more lately expressed, is the opinion of Dr. Samuel Johnson who said of a woman expressing any talent (he spoke in particular of preaching) that it "is like a dog's walking on his hind legs. It is not done well, but you are surprised to find it done at all." A paraphrase of this sentiment is that if a woman expresses a talent, it is not expressed well, and, what is more, people are surprised to find a woman able to express a talent at all.
Woolf ties this into her central point that a woman needs money and space to call her own in order to realize her genius. One of the ties is that she asserts a woman expressing a talent of her own "would need thick gloves on her hands, and bars to protect her of solid gold." (She was speaking specifically of a woman developing a theory of "men's opposition" to women.) Another tie is her analysis that middle class women who began to write, such as Aphra Behn, paved the way for then present day women writers, like herself. They paved the way for Woolf to speak out and "say to you to-night: Earn five hundred a year by your wits." Another tie to her central point is her discussion of how early women writers had to "write in the common sitting-room," which leads to her admonition to have a room to oneself.