My Apple ID account won't allow me to remove my card on file

See -> 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 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) 

Hello ~ If you have any active subscriptions up you may not be able to remove it. Do you have another payment method you may add and then remove it? Post back should you need further assistance. In the meantime clicking on the link below…

Add a payment method to your Apple ID - Apple Support

I hope this helps.

~Katana-San~