why does Adobe refuse refunds? one more poor student getting strong-armed

There are no refunds beyond the 14 day introductory membership term.  After that, fees are deducted from your account monthly or annually until you cancel.  That is what you agreed to.  Your expiration date is available 24/7 by logging-in to your online account.

https://account.adobe.com/plans

You may cancel early and pay a 50% early termination fee or avoid fees and wait until your 12th month of service to cancel.  Your choice.

How do I Cancel my Subscription?
https://helpx.adobe.com/manage-account/using/cancel-subscription.html
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Subscription & Cancellation Terms:
https://www.adobe.com/legal/subscription-terms.html

CONTACT ADOBE SUPPORT:
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Online Chat: https://helpx.adobe.com/contact.html?rghtup=autoOpen
Phone M-F, during normal business hours: https://helpx.adobe.com/contact/phone.html

By the way, it is standard practice for card issuers to accept existing payment contracts for a card that is cancelled for another reason. They do this for your benefit - you can't assume every payment will be stopped or use it to stop payment. Adobe don't necessarily even know - they just are able to keep using the permission you set up.

I appreciate the reply.

the point re Adobe accessing a new account with the cooperation of my financial institution is alarming though. I am so turned off by what I've learned about Adobe's business practices today, they've lost a customer for life--just a user-to-user thought there Bob.

for the record, there is precedence to the idea that if a term of the contract is particularly onerous, the party looking to enforce that term must prove the other party was aware of the term through either their reading of the specific term or through direct notification of the specific term (Tilden Rent-a-Car v Clendenning, 18 OR (2d) 601). I'd say a means of surreptitiously gaining access to my credit account is a pretty onerous term, what would I know though I'm just a student 😉

This is a user to user forum.  We can't address account issues. I am not an Adobe employee, although on occasion an Adobe employee will appear here.

I can say that if you read the agreement that you signed, it provides for Adobe to access another account if the original charge card account is changed and your financial institution cooperates with Adobe.

Please go to Adobe Customer Service (make sure to sign in to your Adobe account first and allow popups on your browser):
https://helpx.adobe.com/contact.html?rghtup=autoOpen will automatically open the chat window.
Type "Agent" in the chat box to bypass the chatbot and be connected to a person.

You may also be able to contact Adobe by phone:
https://helpx.adobe.com/contact/phone.html