How come every time I add a payment method it says I have a billing problem

Verify your payment information, you need to -> Sign in to your Apple ID account page and edit / update your Apple ID details -> https://appleid.apple.com                                                     

• On the Sidebar click Payment methods -> then tap Payments Methods and tap Manage payment method.

Or see -> Add a payment method to your Apple ID -> Add a payment method to your Apple ID – Apple Support (UK)

• If you want to change your card, you need to add first the new card, then remove the old card.
• or if you use your Apple Account balance, you need to set your Apple Account balance as your default payment.

If you update your payment method or add funds to your Apple Account balance, It would take about 1 to 3 business days in order to process.

If you're still unable to update your payment method, Contact Apple Support.

See also the following Apple articles:

Payment methods you can use with your Apple ID

Payment methods you can use with your Apple ID – Apple Support (UK)

fyi: Not all credit & debit cards seem to work with App Store / iTunes Store, try a different one, or preferably a credit card.

If your card is not accepted as a paymenf method, you need to contact your bank.

Remove a payment method from your Apple ID -> Remove a payment method from your Apple ID - Apple Support

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If you can't remove a payment method

If you have subscriptions like iCloud+, have an unpaid balance, or you use purchase sharing, you must keep at least one payment method on file.

• Do you have a subscription? You can cancel iCloud+ and cancel other subscriptions from Apple. When your subscription period is over, remove your payment method.
• If you're in a Family Sharing group and you use purchase sharing, the family organizer must have a payment method on file. If you're the family organizer, turn off purchase sharing, then remove the payment method.
• If you have an unpaid balance, you might not be able to remove a payment method. Instead, change your payment method.
• If you still can't remove a payment method, contact Apple Support.

If your payment method is declined in the App Store or iTunes Store, see -> 

If your payment method is declined in the App Store or iTunes Store - Apple Support

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How to complete your purchase if a payment failed or was declined

1. On your iPhone or iPad, open the Settings app.
2. Tap your name.
3. Tap Payment & Shipping.
4. Add a different payment method and remove the old one. 
5. Try to complete your purchase.

If you still can't make a purchase

• You might have an unpaid order. Learn how to pay an unpaid order.
• Contact your financial institution. 
  • You might need to ask your financial institution to allow international purchases on your debit or credit card.
  • If you want to know why a debit card, credit card, or other payment method was declined, speak with your financial institution. Apple doesn't have information about why the payment method was declined.
• In some countries and regions, your payment method might be declined because of changes to local law. Learn about billing and purchases in Europe or what to do if your card is declined in India.
• Still need help? Contact Apple Support.

If you need to change or update your Apple ID payment method

If you need to change or update your Apple ID payment method - Apple Support

If you still need help, get more help and assistant from Apple directly, see Contact Apple for support and service -> Contact Apple for support and service – Apple Support (UK)