I have had my Photography Plan for over 1 year but cancellation prompts a $65 charge.

We would expect this, since the 12 month terms renews each year, and the fee is half what is left in the current year. But you say on Adobe's site it says that after 12 months there is no charge for cancelling this plan. Can you please share a link. If Adobe are indeed saying this, even by mistake, you may have a strong case. 

So why am I being told I'll be charged this cancellation fee?

By @jamesr79732407

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I'm guessing because you didn't cancel in your 12th month (November) and it auto renewed for another year beginning in December?  

Adobe customer support handles matters such as this on a case-by-case basis.  If you're nice, the agent might be persuaded to waive the cancellation fee.

Good luck!

Log-in to your account below.

https://account.adobe.com/plans

When is your current plan's renewal date?

To avoid a 50% early termination fee, wait until your 12th month of service to cancel, before it auto renews for another year.  Set a reminder on your smartphone or Google Calendar.

Hope that helps.

there are 3 ways to contact adobe; chat, phone and twitter:

chat:
use a browser that allows popups and cookies, and click here, https://helpx.adobe.com/contact.html?rghtup=autoOpen
in the chat field (lower right), type AGENT
be patient, it can take quite a while to reach a human.

phone:
https://helpx.adobe.com/contact/phone.html

twitter:
tweet @AdobeCare

p.s. if you're contacted by anyone (via email or private message), it's much more likely to be a scammer than an adobe representative. ie, double check for an employee badge if contacted in the forums and look for an adobe.com domain in the email address if you click reply to an email. then check again and be very suspicious. any other method of contacting (or offering to contact you) is almost certainly a scam, https://community.adobe.com/t5/using-the-community-discussions/staying-safe-in-the-adobe-support-community/td-p/12919684/redirect_from_archived_page/true