You're asking to prove a negative.
Prostitution exists. Some countries, like backwater republics, the ones run by religious clerics, and the USA, implimented a rule that said "you can't do it". Others controlled it, but let it be.
You, being brought up with this backwards thinking, cannot get your head around it. I understand. If you ever left home, and by home I mean your country, not your front yard, you may see it in action.
You may not agree with it. Certainly, I don't. Don't agree with abortion either. Or, making burgers with enough sodium for 1 1/2 days. Or wearing too much make up. Don't ask for laws to enforce those though. In my country, and most countries run by a democracy, adulthood starts at 18, and we allow people to **** up on their own.