In what way does it just refuse? If we are to help you we need specifics. Quote exact error messages or give use a detailed description of the steps you are taking and where it fails to behave as expected.
To find out how to remove a payment method, or if you can't remove your last payment method or use no payment method with your Apple ID, read this article --> Remove a payment method from your Apple ID - Apple Support
- Ongoing subscriptions and Family Sharing organizers must always have a payment method present. To edit the cards used for those you may need to first add the new card and make it the primary payment method before removing the old card ( If you need to change or update your Apple ID payment method - Apple Support ).