I'll play a bit of devil's advocate here, 'cause I think it might help the debate. (I do find it slightly ironic that to play devil's advocate I need to speak against prostitution, but I digress.) First, if I'm not mistaken, there aren't legal brothels in Vegas. I think there's a law in Nevada saying that any city with a population over X can't have brothels, this was targeted against Vegas.
But there are some legal brothels in Nevada and this doesn't really weigh into arguments for or against prostitution.
As far as reasons to be opposed to prostitution without bringing God in.
The degradation argument. This is more of a values question, but one that I don't think you need to have a faith in a higher power to have. Ultimately you're putting a price on sex which to many is an act that ought to be reserved for couples in an intimate relationship. By cheapening sex through putting a price tag on it, it could be perceived as devaluing the importance of exclusivity in a relationship. Some might argue that what other people do in their private lives should not effect their relationship, but there is an argument to be made about society itself. A society that condones casual sex reflects upon all members of it, even those who disagree.
There are other factors that come into play. For example, there are concerns of sex-trafficking. If you legalize prostitution and advocate brothels, there is still a great risk that organizations in the Balkans, the Chinese Mafia, and the Russian Mafia might ship over women to be sex-slaves to the country that legalizes it. With a bit of clever forgery of documents, they could pull this off in spite of the heavy regulation. This would just further build an evil that exists that so rarely is discussed. These aren't women who are willing, but forced. And that is degrading.
It's true that men can be prostitutes too, they're called gigolos. But the other larger principle behind this 'degradation' argument is that it devalues the
person. By allowing folks to induldge in casual, paid for sex it objectifies people as naught more than objects of pleasure rather than a human being. This mindset sticks and can often result in less healthy relationships with other people outside of the confines of the brothel. There is
scientific evidence that backs this principle.
Disease and pregnancy argument. You can test all the clients as well as all the prostitutes weekly, but some will slip through the cracks as far as disease is concerned. Granted, those who play with fire are oft to get burned; but this is something that can't really be stopped. But why should this matter? If a person is willing to knowingly risk an STD/STI, why should we stop them?
Because they have already shown a stupidity and callousness toward the risk. If a client transmits a disease to a worker, that person's occupation is finished and they have just become a risk to everyone they have had sex with up until the discovery and unless treatable everyone in the future. If a client contracts a disease, the odds are that because they were willing to risk contracting the disease, I wouldn't be at all surprised if they transmit it knowingly or unknowingly to others not involved with the prostitution in the first place. It poses a grave danger to society and isn't an issue that should be glossed over.
And whether you're fine with abortion or find it reprehensible and seek to see it made illegal, there will be a lot of pregnancies. Granted there will be contraception used in a legalized brothel, but a sad fact is that the only guarantee against pregnancy is abstinence. (With the possible exception of Jesus, if you believe in him) Abortions have a lot of consequences that are long-lasting beyond the procedure. Sure the woman who was doing the job / was the client should understand that risk, but while many of us might advocate the legalization of abortion, surely we can agree that there ought to be less of it.
How prostitution works argument No this isn't a technical 'when a man pays for a woman' speech, it's the mechanics and institution of prostitution. I refer specifically to Pimps. Put simply, they would need to go. They do objectify women as their property. The women are expected to pay up. What's worse, Pimps solicit, manipulate, and coerce underage women into prostitution. They are essentially kidnapped, operating on a street corner in a redlight district. If they try to escape, they would suffer the consequences.
Pimps are the biggest problem with prostitution. If prostitution were legalized, each man/woman would have to work as an independent contractor. There would need to be a union that ensures their members receive regular check ups so that they're clean. And having a 'brothel' in the sense that there is a place folks can go to seek a prostitute is fine. But ultimately the 'boss' would need to be the sex-workers themselves and not some boss who choses their clients and takes a cut.
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All of that said, I'm not opposed to the legalization of prostitution. It's an issue that I don't much care about. But I do think it's an issue people should be educated on.