You may want to take Tunisia, Morocco, and Algeria out of the Middle East, but I wouldn’t. They are much more similar to Egypt, Libya, Saudi Arabia, Iraq, etc. ethnically, culturally, historically, religiously, and politically than they are to any European country or to the sub-Saharan African countries.
The Bush admin used the term "The Greater Middle East " to to include all of North Africa and the former Soviet states with high Muslim populations, the term did not really catch on.
I don't see this as anything to argue about.