I noticed that my wife's Avast Security for Mac was connected with my Avast account, and I thought I'd install a fresh version in her name. Ran the uninstaller, but got caught in a loop. I get a notice saying "Uninstallation complete" and "reboot is necessary." After rebooting, there's a notice asking "Uninstall Avast?" Clicking "Uninstall" just repeats the process, and if I cancel and run the Avast Security.pkg installer, I get an installation error: "Avast is already installed, please uninstall the previous version first."
I tried deleting the existing Avast application, but that didn't change anything. (And now I see that you advise against do so.) I searched the forum, and found Ondrej Kolacek's advice to run rm -rf "/Library/Application Support/Avast" in Terminal, but that didn't help. (I noticed a lot of "permission denied" statements in Terminal's log. I'm not savvy enough to understand what was going on, there.)
So at this point, my wife's Avast protection is broken, and nothing I try seems to help.