Apple requiring a payment method such as a credit or debit card, even for free apps or where you have enough account balance to pay for the item, is not an uncommon observation. Some possible reasons are outlined in the links below such as outstanding balance, an issue with a payment method you have currently entered, ongoing subscriptions, or simply because they say so. You can try to configure your account to not have a payment method but you may find there is no option other than to enter a valid payment method to satisfy one of Apple's requirements. If the item is free you will not be charged. If it costs something, your Apple ID balance will in most cases be used first. You can later try to remove the payment method and see if it only needs to be there temporarily. This might satisfy your parents if they are concerned about you having open access to their card.
If you can’t download or update apps on your iPhone or iPad - If you can’t download or update apps on your iPhone or iPad - Apple Support
- "You might need to have a payment method on file, even if the app that you want to download is free." If you have something else on your account that requires a payment method, such as a subscription, and your current payment method is not working then Apple won't let you download even free things until you fix the payment method. This is explained in this document, 'If your payment method is declined in the App Store or iTunes Store' - If your payment method is declined in the App Store or iTunes Store - Apple Support
If you can't remove your last payment method or use no payment method with your Apple ID - Remove a payment method from your Apple Account - Apple Support
- If you have any active subscriptions, you must have at least one payment method on file other than Apple ID credit.
- You might not be able to remove a payment method if you have a balance due.
Sign in to your Apple Account on the web or in your device settings - Apple Support - at the very bottom: "When you sign in to the App Store and other media services for the first time, you might need to add a credit card or other payment information."
Also:
How App Store and iTunes Store purchases are billed - How apps, content, and subscriptions from Apple are billed - Apple Support
Some purchases aren’t charged to your Apple ID balance
- You can’t charge gifts to your Apple ID balance. If you send a gift or gift card, your primary payment method is charged.
- Some subscriptions might not be charged to your Apple ID balance.
And:
What you can buy with your Apple Gift Card or Apple Account balance - Apple Support
"Some purchases might require that you have a credit card on file, even if you use your Apple Account balance to make the purchase."
So, the resolution will be to add a payment method:
This document explains how to change, add, review, or remove Apple ID payment methods on a Mac or Apple mobile devices; click here --> Add a payment method to your Apple Account - Apple Support
Another option would be for a parent to create a family Sharing group with you as one of the members. They would have to add a payment method, but if you qualify for having Ask To Buy added to your account, they would have control over spending that could end up being charged to that card.
To learn how to set up Family Sharing, read this support article --> How to set up Family Sharing on your iPhone, iPad, or Mac - Apple Support
And about ATB:
Approve what kids buy with Ask to Buy - Apple Support
