He'll Getcha with the Title

"More Sex is Safer Sex" by Steven Landsburg was interesting: he presented a number of different solutions to very complex problems, he addressed some captivating topics, and used math, logic, and rational analysis to prove his points. Here is my problem: his reasoning, deductions, and lines of thought are infallible - everything makes sense. Until the very end of his argument. Everything is in order, everything is scrupulously analyzed and dissected, and everything leads directly to a logical conclusion. But the conclusion isn't right. I still cannot fathom how the argument falls apart at the very end, even though every single detail makes 100% sense. I guess his assumptions are incorrect... So it goes.