It's an emotional problem. If people saw sexual intercourse for pay differently the solution would be different. But they don't. They see it as a form of personal subjugation and abuse because it is physically invasive and it is not voluntary. It is coerced. And that degrades and dehumanizes everyone involved. The only possible argument for legalizing it would be for the sake of individual freedom of choice. But the fact that consent has to be coerced pretty much eliminates that justification. So now all you have left as your argument is your own indifference. You claim there are no victims because no one is "innocent", and the damage is invisible and minimal (to you). But a pedophile claims the same thing to justify having coerced sex with a child.
All you really have to stand on is that you don't think people are victimized by participating in prostitution. But try getting a job with that on your resume. Try renting an apartment. Try finding a spouse or raising a child. When was the last time you dated a prostitute? The damage from participating in prostitution is deep and far-reaching. And that's just the prostitute. Lets consider the 'Johns'. The psychological issues of having to pay people to pretend to be intimate with you, and with thinking their bodies and their sincerity are a commodity that you can take away from them for a price.
A few thoughts come to mind while reading this and other posts on this thread.
One thing is that there is an oversexualization in society overall - not just with prostitution, but even with legal activities - such as one-night stands, going to singles bars (often referred to as "meat markets"), strip clubs, skin mags, phone sex, webcam sex. Even movies and TV (even if rated "PG") tend towards a bit of lewdness designed to titillate the oversexed viewing audience. It can even be discerned in TV commercials and other advertisements. Sex sells.
This seems to be across the board throughout society, although some areas tend to be more conservative than others.
Personally, I've never been to a prostitute, although I have been propositioned a few times by prostitutes, whom I've had to politely turn down. I would never coerce anyone, although if I had accepted their offer and paid them for sex, I can't see how it would be coercion - especially if they approached me first. There may be other situations where a man is out of town on business, has a drink in a local lounge, where he might be approached by a lady of the evening. He may not go out actively looking for a prostitute, though. Some women can be quite sexy, seductive, and know how to use their feminine wiles to get what they want from a man. This can often happen even without actual monetary exchange.
Oftentimes I see commercials for a local jeweler, which usually shows a man giving a diamond ring to his wife/girlfriend/fiancee - and she just suddenly melts with passion. This is how people are conditioned in this society - and it might very well be degrading and dehumanizing. Although that seems more a comment on the obsession this society has with sex and money - but of course that's nothing new in human history.
Whether or not prostitution is legal or not - this is just a technicality and likely does not change the overall condition one iota.