I was pleased to see an acknowledgement of International Women's Day in the musical blogosphere. In his take on why "there are so few female composers" Tim Rutherford-Johnson provides a list of mostly living 20th and 21st-century composers who have written avant-garde music (that has been recorded). His idea that the lack of teachers and mentors is responsible for the dearth of female composers (there isn't a dearth, by the way) misses the mark.
Nadia Boulanger was, by all accounts, the most important composition teacher of the 20th century. She was also an excellent composer, but she stopped writing after the death of her sister Lili, who was, even as a very young person, one of the finest composers of the 20th century, of either gender. One of the reasons I think Nadia Boulanger devoted herself to teaching rather than to composition was that she felt that, perhaps, she could help develop other composers develop the way she helped Lili develop. Many of her students were women (you can find an incomplete list of her students here.) In addition to her composition students there are a large number of analysis students on the list. A great part of teaching composition is teaching analysis.
From where I sit in the 21st century I can clearly see an early-20th-century trend involving the rise of women as artistic and literary figures as well as important figures in the sciences. (Madame Curie and Rosalind Franklin are two examples that come to mind). And then somewhere in the middle of the century, perhaps around the time of McCarthyism and the prominence of Virgil Thomson as a music critic (click here for google search for the term Virgil Thomson and Misogyny, though most of the material that comes up is from Google Books) women were forced back to the margins of creative culture.
Marion Bauer is an example of a first rate composer who fell victim to Thomson's mysogyny. He deemed her too conservative to be considered an equal to the 20th century composers he admired. I imagine that he found her to be intimidating (she was a far better composer than he was), and that he used his power of influence to try to take her down.
A couple of female-friendly decades followed Thomson's death (friendly to women who were composers and women who did other creative things), and though we don't yet have an Equal Rights Amendment to the U.S. Constitution, at least as of 2009 women are legally entitled to get equal pay for equal work.
I fear the the neo (or pseudo) McCarthyites that have invaded the second decade of the 21st century are trying their darnedest to marginalize women once again. With the marginalization of women as composers, even retrospectively, (and even inadvertently) comes the marginalization of the contributions of women to the greater culture.
My short answer for what a 21st-century female composer needs to succeed? The big ones are talent, technique, time, and a support system. It needs to be a financial support system as well as an artistic one, and it needs to provide opportunities for a composer who is a women to be able to hear her music performed. And she needs to hear it performed more than once. She needs to have critical feedback from people who know what they are listening to, and she needs to have her music evaluated in the same way that her male counterparts have their music evaluated. She needs to learn first hand, and in proper acoustics, what works and what doesn't.
Teachers and mentors she has. It is opportunity that helps her grow as a composer.