The name of the book represents one of the main statements that the author gives to the reader, discusses it and then represents it from economics point of view. It is true that the AIDS virus would spread less quickly if there were less monogamy, chasity and other forms of conservativity in sex. Because if uninfected people will have more sex that means that the possibility to have a partner with AIDS reduces. Nowadays there are many AIDS-infected people in the world (including those who don't know that they are infected), who still have sex with different people, and, at the same time, many uninfected people prefer to be monogamic to avoid the illness. So, people don't care about doing bad things and causing negative externalities but only seldom there are volunteers to do good things (which will cause positive externalities) without being payed and rewarded.
Through the first part of the book the author continues developing this idea, giving other, more complicated and less evident, statements. For example, did you know that the most charitable people support the fewest charities? Rubbish, you say? No, it isn't.
Everything in this world is somehow connected with economics; every action has its spillover effects, which sometimes cannot be predicted or be taken in account - even a birth of a baby.
People relationships and competition with each other are also a good example of how Mr. Landsburg represents some economics statements to noneconomists. Why do people want a promotion? To get a new status or to increase wealth. But why, when people reach a particular level of income, when it is enough money to live, buy good quality things and even travel n times a year to diffetent countries with their families, they don't stop and still want another promotion? The answer is simple and obvious: because 'that guy from the office' has a bigger car and a better house. It's people nature - we compare our wealth to the wealth of the others and, unfortunately, very often are not happy with the results. But if people don't know that somebody lives better, they are happy with their wealth.
All those things and many other interesting questions are explained in the book "More Sex is Safer Sex".