You're thinking like an engineer. From the perspective of the bank, you (the individual) has given a merchant (gym etc) a standing authority to bill you. That authority is between you and the merchant, not between your specific card number and their payment processor. Having your card reissued is not a withdrawal of that authority.
Based on the brief detail provided, I think OP's mistake was to cancel/reissue the card rather than dispute the charge / block the merchant.
Re:The scam that is Visa Account Updater
by kasey_junk on Thursday June 26, 2025 @07:13PM
(#44392363)
If you are using a credit card you aren’t using “your” money. And it’s absolutely the card issuers business to be an arbiter of who is using their money.
That's an issue between me and the merchant. I don't want MY bank acting as an enabler for the merchant over my wishes, with my money.