This is my first day of having Avast, and I hate it already. I agree with others that it seems like a scam. However, I think I have found the answer to this question... sadly, some 2 years after the OP asked it and never received an adequate answer.
When I purchased a year of Avast Internet Security (plus yes, I did try Grimefighter because I have been having some PC issues and want extend the life of my computer a little longer before I have to buy another, and hoping this will improve its performance), it went through this thing Digital River, and I was given no choice at all to opt out. If I wanted the software, it said clearly on my purchase page that I would be automatically enrolled in an autorenewal program - which I think is about the lowest thing a company could ever do to its customer. What that would likely mean for me, is well after I've forgotten about the details of this purchase, and well after I've stopped using the card I put it on (but did not cancel said card), I would receive a charge I did not ask for, I would then not pay it because as far as I'm aware I am not using that credit card, and my perfect credit would be destroyed over some POS scam like AVAST. So, extremely not cool, and Avast has lost major points with me. Much worse, I have wasted 2 hours of my time trying to figure this out, because Avast goes out of their way to not tell you anything about it, and the account home page is totally worthless, with no useful settings I can change whatsoever. [Plus, why is there a picture of an American flag that says "Europe, English," and a Canadian English, and yet another Europe, English?? There is no such thing as the US?... The means for even installing this nonsense was made far from clear. So clearly this company is far from intuitive and user-friendly, which is surprising given the great ratings they had which prompted me to buy it. OK, no time for ranting... back to the topic at hand.]
However, for those who have been affected the same way I was, here is how you get out of it:
Find the email you received for your new Avast subscription. It will have a password on it, an order ID #, and if you scroll towards the bottom, there will be a paragraph about the autorenewal called "Auto-Renewal Plan Terms." Near the bottom of that paragraph, it says "You may cancel your auto-renewal plan at any time by logging into the My Subscriptions portal." The phrase "My Subscriptions portal" is a link - you must click on it, there is no other way to access this autorenewal anywhere, and you certainly can't get to it from within your Avast account.
In my case, this is the link, but I can't guarantee you it will be the right link for you, seeing as it is specific to my country and language, etc.:
https://store.avast.com/DRHM/store?Action=DisplayCustomerServiceOrderSearchPage&SiteID=avast&Locale=en_USOnce there, you need to enter the order ID# and password sent to you in that email. From there, you can click on the blue button "Manage Subscription."
For some strange reason, when I did so, it said my subscription was already on Manual, with Auto-Renewal Off. So maybe this is yet another glitch with Avast, and not actually something that will happen to most customers despite the claims on Avasts' purchase page that it will happen to you without choice. I don't know. I just know they told me it would Autorenew, and then when I went in to change that, it seemed that I had wasted 2 hours researching this for nothing. Whatever. At least it says it's off, so hopefully I will not be charged by these idiots.
A note, it would seem that the Autorenewal function does not affect programs outside of the actual anti-virus ("Internet Security"), since there is no place to log in for Grimefighter, etc. So if you purchased an additional program, it would seem that these are not auto-renewed since they are not seen as essential, just Internet Security. Still obnoxious, and even more so if you bought a multi-year subscription so that this will REALLY be a surprise when the time comes.
Hopefully, this explanation will help others who read that fine print on their purchase and were like - wait, WHAT??! Hopefully my wasted morning will save you a little extra time.