The argument in favor of a “teen wage” is based on the fallacy that employers will hire employees they don’t really need if they can save some money. The truth is that employers hire only the employees they actually need to run their business and they pay what they have to pay to make their business work. Lowering wages does not materially increase the employment of unskilled workers.
The second fallacy is that a job at any price is a good thing. If that were true why not pay $1/hour or $.10/hour? The fact is that people would rather not have a job at all than take one that is not worth doing.