The strongest argument against prostitution, no doubt, is its alleged immorality. If this means no more than that most people THINK prostitution is immoral, that appears to be correct. But if this is taken to mean prostitution actually IS immoral, then an argument is required. Believing something doesn't make it true. That the Sun revolves around the Earth, which is immovable, are examples of false beliefs that once were widely held.
That an activity is illegal does not establish that it is immoral, any more than than its legality establishes its morality. Ownership of slaves, among the most immoral of all activities, was legal before the passage of the 13th Amendment, but illegal thereafter, even though its moral status did not change. What is legal can be ascertained from statutes in books of law, while the morality of an action presupposes a suitable standard.
There are many claimants to that role, including subjective theories, family-value theories, religious-based theories, and culture-relative theories, according to which actions are right when you (your family, your religion, or your culture) approve of them. So if you (your family, your religion, or your culture) approve of incest, cannibalism, or sacrificing virgins to appease the gods, those actions cannot be immoral. They are moral, necessarily!
All of these approaches make morality a matter of power, where right reduces to might. If someone approves of killing, robbing, or raping you, you have no...