If you don't want to give your teenager access to your user / Creative Cloud account, he/she won't be able to use it. You'd need to obtain a separate subscription for them.
I suspect that the issue is that Adobe likely doesn't issue Adobe IDs to children under 13, because of COPPA. Given the nature of Adobe's products, the potential legitimate userbase of under-13s is small, and the compliance costs could be very high. Bear in mind that a kid under 13 can't legally sign up for a Facebook account, with or without parental permission, either, because FB doesn't want the liability for compliance if it knowingly signed up under-13-year-olds.