re: My 15-year-old kid wants to start dropshipping

First, congrats on having a 15 year old that is showing some entrepreneurial business initiative, and thinking beyond a 15 year old. Second, do not squash his confidence and initiative by dismissing it. Use this to further his education of business by making him provide the research and outlining the positive and negative of his plan. Pay him to do the research if you can.

As for drop shipping, this is basically what most online shopping sites are these days. The person selling the merchandise is not the manufacturer or keep an inventory, they just sell the merchandise using their marketing skills and business sense. The perils are dealing with returns and credit card charge backs.
The other peril is that the sites he sells through will make it easy and take care of the transaction headaches, but the seller has little control over returns, charge backs, and cost of return goods.

If he has thought of all the negative and has a good plan for it, let him try it out small and see where it goes.