I believe because this is a core package the system is hickuping over removal
since there will be no default browser. (e.g. update-alternatives)
To see current default (should be aBrowser):
sudo update-alternatives --display x-www-browser
To change this see here:
https://wiki.debian.org/FAQ/Gnome
You can try setting Midori as default while you reinstall aBrowser.
sudo apt-get install midori
Then see debian FAQ above on setting it as default.
For complete removal and re-install of aBrowser let's try...
sudo apt-get remove --purge abrowser
Delete .mozilla/abrowser/ in your home directory, should it still be there
Delete /etc/abrowser/, this is where your preferences and user-profiles are
stored
Delete /usr/lib/abrowser/ should it still be there
Delete /usr/lib/abrowser-addons/ should it still be there
Then to install it again:
sudo apt-get install abrowser
sudo apt-get update && apt-get upgrade (just to be safe and up-to-date.)
And use Debian FAQ to set it as default.
If that still doesn't work there are some more down and dirty methods of
forcing it to bypass the error, but I'm hoping that will work for you. :)