There are a number of different reasons why you might prefer to get prepaid credit cards for teens. It reduces the chance that you or they will accumulate large balances by governing how much they can buy. This sort of prepaid Visa cards and can help them learn to manage their money while still allowing the convenience of being able to pay with a credit card. It allows you to check what purchases they are making as well. Most importantly, teens can start working on their credit rating.
If your teen has started asking you for a credit card, it might be best to start them out with one of the prepaid visa cards that are available. This allows them to use credit safely. Once they have shown themselves to be responsible and to be able to properly manage their money you can then consider helping them to get one of the student credit cards that are available, but the prepaid cards are a great way for them to learn to budget their money properly and use credit cards.