When I start airgeddon, I see this message "A graphical X window system has not been detected. If you already have one, check it's working properly. It's essential for airgeddon. The script can't continue"
That message is shown when airgeddon is not able to connect to your X Windows System for some reason. Maybe you have a restricted configuration. Try to launch the command xhost + before launching airgeddon. That should fix the problem.

xhost +