In "A Room of One's Own" by Virginia Woolf, what is the main argument, topic or symbolic meaning of her discussion about "What if Shakespeare Had...

The question of Shakespeare's imaginary sister, Judith, was raised by Virginia Woolf in her 1929 essay entitled "A Room of One's Own." As a writer herself she was painfully aware of the educational differences between her brothers who were formally educated and herself; educated at home, she felt strongly about the lack of opportunities for women in literature in her own era. Woolf wanted to raise awareness by encouraging discussion about the possibility of a female equivalent to Shakespeare in Shakespeare's day and how much more difficult it would have been then for a female to be recognized, let alone admired. Just as it would be difficult to imagine an existence without the presence of Shakespeare, it is almost equally impossible to imagine what talent was lost, overlooked or unable to develop to its potential simply because it was not the work of a man.  

The main argument of chapter three of A Room of One's Own, where Judith Shakespeare is discussed, centers on the fact that it is the opinion of men that influences trends and it is men who believe they know what women want and aspire to. It is a "masculine complex," that ensures that men remain superior. This contributes to women's lack of opportunity because a great writer, or the greatest writer, has to be free from material concerns and has to be able to devote himself or herself entirely to their work; this allows for complete freedom of expression. Women cannot attain this because they have to concern themselves with appearances. Many men cannot fulfill their full potential either as they concern themselves with protecting women. Notably, it is the opinion of a man that "The desire to be veiled still possesses [women]," suggesting that women have no such ambition anyway.

In Shakespeare's day, women were "imaginatively" crucial to many story lines; they were strong and influential characters in those stories, whose words were significant and around which many plots and themes revolved. Yet, in reality, Woolf points out that a woman "could hardly read, could scarcely spell, and was the property of her husband." This, therefore, is the reason women would not have been able to reveal their genius and not because of any lack of talent. In fact, a woman in the sixteenth or seventeenth century, Woolf contends, would no doubt "have lost her health and sanity" because she was unable to reveal her true self and her potential for great writing. She would have had to attribute her work to "Anon," or, later, perhaps pass herself off as a man as George Eliot did. Unfortunately, this anonymity or non-disclosure unwittingly supports  and perpetuates the injustice. 

Woolf confirms this argument by pointing out that even for men who are not wealthy writing is still a possibility— fraught perhaps with uncertainty and unpleasantness but still possible. There is an air of indifference surrounding the writing of men, until the point where they become great. However, for a woman without "a room of her own," writing was and still is not only unlikely but without any purpose at all. As she says, "Write?" What's the good..."