Unable to remove my payment method

You can't choose None as a payment method...

1. If you have an unpaid balance or payment due
2. If you have a subscription that automatically renews
3. If you're using the iTunes Store or App Store for the first time
4. If you are not in the country or region you’re creating an Apple ID for
5. If you changed your country or region
6. If you're a part of Family Sharing

See this Apple article: Change, add or remove Apple ID payment methods

Change, add or remove Apple ID payment methods – Apple Support (UK)

You need to add a valid new card before you can remove the old one.