Apple generally requires a valid payment method be added to the Apple ID in order to make use the iTunes and App Store services. It can normally be avoided if there are no pending payment or active subscriptions on the account.
The fact its requiring one now means there is some charge or subscription that requires it now on your account. Once that happens, you must add a verifiable payment method to your account. no way around it now.
Once the pending charge or active subscription has been correctly charged, you can request a refund, and then remove payment method from your Apple ID and it should not ask for it again unless a charge cannot be completed for any reason.
click here ➜ If you want to cancel a subscription from Apple - Apple Support
then here ➜ Request a refund for apps or content that you bought from Apple - Apple Support
then here ➜ Remove a payment method from your Apple ID - Apple Support