What argument is Woolf making about all the works that are signed “Anonymous” throughout history?

In A Room of One's Own, Woolf argues that it was "the sense of chastity" which drove women, as late as the nineteenth century, to publish their works, not necessarily anonymously, but with the names of men appended to them. Woolf points out the fact that such great nineteenth century writers as George Eliot and George Sand chose to conceal their sex in publishing their writings, as a means of "veil"ing themselves. This was partly, Woolf argues, because society deems a desire for publicity to be wrong in a woman—"anonymity runs in their blood." Women are not concerned with fame in the same way that men are. As such, Woolf wonders whether there may indeed have been plays written by women during the sixteenth century, but which were left "unsigned" because any female writer of that time would have preferred to live a "free life," without being concerned with how her work would be perceived. Woolf suggests that women writers choose to conceal their identities because they know that they will be judged far more harshly if they reveal their sex. This, combined with the fact that women as a sex are not as concerned with fame and reputation as men are, leads Woolf to conclude that most anonymous works may indeed be the works of women.