The “declining” is often done by the bank that issues the card. There’s a lot of card fraud pretending to be from iTunes/App Stores, so banks are a bit skittish. Call your bank to find out if/why they declined it. To read more about declined cards:
https://support.apple.com/en-us/HT203005
The reason you can’t delete your card is because your account requires a valid payment method at all times. With just one card, you should add it as if it were a second card, is accepted, only then delete the “first” card.
You can also change your account for no-credit-card type, but you won’t be able to buy anything unless you add Gift Card credit to the account.
Create or use an Apple ID without a payment method:
https://support.apple.com/en-us/HT204034