I contacted support as prompted on the Adobe Store when I tried to cancel my plan. The first thing they do is to offer a free 3 months to keep you as a customer, but it requires you to start a new plan. When I asked to reject the offer, they introduce scare tactics like "you will be charged an early termination fee" but they always beat around the bush when I tried to ask when exactly am I supposed to cancel and when is my next annual renewal. The customer support agent simply cancelled my plan in the end and ended the conversation, which I felt was unnecessarily rude. It's a terrible experience and I'm never coming back even if I needed such software again.
Cancel within 14 days of subscribing to avoid cancellation fees.
If the subscription has started or run for some time, cancel within 14 days of the date the subscription is supposed to end to avoid a cancellation fee. For example, if the subscription is supposed to end/renew on, say, December 31st, you can cancel anytime between December 17 and December 31.
If you cancel at any time before the end of the subscription outside of the 14 days before its end, you are charged a fee of ½ of the remaining subscription. For example, if you bought the subscription on January 1st, it will end/renew on December 31st. If you cancel in August, you will be charged a fee of 2 months' worth of subscription. More in-depth information about cancelling a subscription and associated fees can be found here:
The 3 free months is a customer retention offer. If you accept it, that means you now have a subscription for 15 months but you only pay for 12. It does require a subscription, however. Adobe isn't going to just let you use their software for free.
I hope the above is useful, and I'm sorry the CSR was less than helpful. There's not much we can do about that.