The ethical challenge with in-vitro fertilization (IVF) is the high loss of life for human beings in the embryonic stage. Also, in favor of the Biblical ideal, many advocate for children to be brought into a solid relationship that has both a husband and wife. As a result the idea of a single woman having a child via IVF is rarely discussed.
Now, however, ethicists from Boston College argue that single women should not be allowed to have IVF as a measure to keep the population down. Read the story: http://www.telegraph.co.uk/news/politics/10988963/Single-women-should-not-get-free-IVF-say-ethics-experts.html