You don't understand how limits on some types of work are different from a comprehensive prohibition on other types of work? I don't beleive you.
The distinction is arbitrary.
Do you think all sex workers identify as female?
> As long as buying a woman just to exploit her body sexually is normalized we will never reach equality
How is it any different from any other industry? What's the difference between paying someone to massage your scalp because it feels good and paying them to massage your genitalia because it feels good? For that matter, how is it any different to any job at all? Is a person being paid to restock shelves being hired for their holistic personhood? We're "exploiting" their body for their ability to lift items onto shelves. How are sexual skills any different from any other skill which we employee people for?
> The few happy sex workers that truly think they are not abused are not worth the enormous negative effects prostitution has on society.
Right, those sex workers are so dumb they don't even know of they're happy or not.
This is clearly a gender specific problem despite your desire to frame it otherwise.
As to your second point, we often hire underage people to do work such as restocking shelves. If sex work is truly the same as retail work would you also argue that hiring an underage prostitute is no different than when Walmart hires a 15 year old to push carts? If not, what's the difference?
This is clearly a situation that society knows how to handle via a fairly wide variety of methods and control systems.
I don't find this argument compelling. Are you saying that the only professions that are morally permissible are those that we would allow fifteen-year-olds to do? We don't allow them to bartend, drive trucks, nor be members of the US Senate, but I find it silly to think that fact makes those professions particularly immoral. 15 year olds aren't even allowed to work 40 hour weeks in most countries.
And, to answer your question, I think the answer is that the fifteen-year-old is not sexually nor emotionally mature enough to engage in prostitution. (Just like they are not mature enough to serve alcohol or drive, whereas they are likely emotionally mature enough to push carts.) They're below the legal age of consent by three years, for goodness' sake! Advocating for legalized and regulated prostitution is not equivalent to advocating for pedophilia, and I find the equivalence you've drawn troubling.