Emily Bazelon is tackling this puzzling question in Slate. I think most arguments about keeping prostitution illegal are stupid, but this one--the one she features most prominently--is downright moronic:

The case for making it against the law to buy sex begins with the premise that it's base and exploitative and demeaning to sex workers. Legalizing prostitution expands it, the argument goes, and also helps pimps, fails to protect women, and leads to more back-alley violence, not less.

Name one industry that has been characterized by more violence and mayhem when it was legal than when it was illegal. For that matter, name one job, other than being a mercenary, that involves as much violence as, say, the drug trade1. You can't, because this argument makes absolutely no sense. Violence goes hand-in-hand with illegal industries because there is no legal way to enforce contracts, and because people engaged in illegal activity are understandably reluctant to report other crimes that took place during their malfeasance.

1You're possibly tempted to say "Taxi driver", but in fact drivers of illegal cabs suffer a vastly disproportionate share of the violence.