Not AARP..
David Weaver
..but I had another affiliated card in the past that wanted to change from visa to mastercard or the other way around and a different bank. I canceled it.
Not because I cared that much, but because they reminded me that I didn't use the card much and I didn't want to go read the new terms to see if they would matter.
AARP generates money off of their members through affiliations - I'm sure sometimes when they change something like that, it's good for you, and others, it's good for them. They won't tell you which it is very plainly, but in your card agreement, I'm sure they have the right to do what they're suggesting.
What I do recall from my card when I got the notice is that I could act within a certain period of time in writing to keep the current card with the same credit processor (I think it was macys - a card that I had from long ago when we used to actually walk into malls and get formal clothes for work - and they actually had a tailor on staff to get a suit and get measured and get it the next day), but it was more cumbersome to go through that than it would've been to just cancel the card. So, I did what you did - I got a different card. And more than four figures in "rewards" since then. Probably not what they were aiming for.
You can send them a letter letting them know why you're getting another card, but they probably won't care. Look up the AARP CFO and send the letter to them, and not to their customer service.