As far as I can tell, her point is this is effectively impossible, at least for a user-facing system. Do you want all the files you wrote in your word processor program or text editor gone when you uninstall those? All the files you downloaded from your browser gone if you uninstall it? If not, there is no reliable way to tell what files are created by a program automatically and which are created by a human using that program. You can easily enough remove everything that was created during the installation process, but not all future changes.
Beyond that, consider other changes, like say you decide to change DNS implementations and then later decide to change your default DNS server. If you uninstall the provider to change back to previous one, do you also want to change back to the old server you were using or do you want to retain that change? Personally, I'd want to only change the provider but keep the new server.
Then consider difficulties with directories shared across multiple machines. Let's say you have /home/${USER} set up as an NFS or Samba mount so you can keep the same files across multiple workstations. If a program respects XDG config dirs and stores stuff in there and you uninstall on one workstation, should it remove the files from all of them? Do you want all your devices to be identical or do you only want the home directory to be identical? There is no possible way for a package manager on a single system to know this.