I love it when a whole bunch of adolescent or younger kids start talking about issues about which they are far too immature to fully comprehend. "Religion is for sheep! Nothing is wrong with prostitution! A single mother is just as effective as a mother and father together!"
Really, people, collective values and relationships are far, far more complicated than you could possibly realize, especially regarding sex. I hate to break it to you, but there is more to life, more to constructing values than simply "not hurting people."
Prostitution is morally repugnant to most people (and I say most people because there are only brothels in some counties in Nevada out of a nation of over 300 million) because it rips away the entire basis of how men and women operate on a civilized level. We are not animals. We resist our base urges. These are justifications that grew out of real, legitimate concerns (such as diseases, unwanted pregnancies, inheritance disputes, and an overall pain in the ass situation to deal with). And when you have a government that supposedly represents society give an endorsement of meaningless, carnal sex, that pisses people off, for good reason. There are a lot of liberties in the US, but these don't constitute any sort of approval (there's no law against masturbation, but try bringing it up in normal conversation). And even though we acknowledge that some people are going to waste their lives gambling, drinking, or other vices, we aren't about to take active measures to provide yet another outlet for deadbeats and losers and in so doing implicitly encourage them to make use of it.
"When the only reason for something being illegal is some assertion that it demeans humanity, but any actual suffering cannot be discerned, then it should be legal."
Sounds like quite an argument in favor of buggery, if you ask me. Or maybe just wanton torture of animals, since they aren't people, after all.