That is why I said: "middle east is not a defined term".
Sure it is, in English at least. English is defined by popular usage, so how people use it IS the definition. What I gave you was my perception (as an American) of how the term is used in this country.
You can also see what Wikipedia has to say about it here:
If you look at the map, you'll see that it pretty much matches up exactly with what I said before. Egypt in, Afghanistan out.
Point is: we define it geographically, and the americans more or less by political reasoning
However Americans have collectively come to use the term "middle east" to mean that group of countries, it IS correct, by definition.
if the regions/countries you mention are "middle east", what is then "near east"
Simple: there is no "near east" any more. No one really uses that term, so it's archaic. We use the term "middle east" now. Decades ago, we used to use the term "near east" to describe the Ottoman Empire's possessions in Asia. There might be some academics who still use the term for something, but that's jargon and not popular usage.
So calling those areas "middle east" makes no sense
It doesn't matter what "makes sense" to you. The only thing that matters is how a term is used in English, if you're communicating with an English speaker. However it's used popularly IS the correct usage. If English speakers worldwide all decided tomorrow to start calling that region "Vulcan", then *that* would be the correct term for the region. Even better, if all English speakers suddenly decided to call that region "Europe", and to call what's now Europe "the Middle East", then *those* would be the correct terms.
So calling those areas "middle east" makes no sense, not even from the point of view of the USA (world map, not political).
Language isn't defined by geographers, it's defined by popular usage. Every language is borne out of the culture of its speakers, and reflects upon their culture and their worldview to a huge extent. This term has obviously come about because of the American worldview and its involvement in geopolitics. The term may not be what geographers would prefer, but there's a lot more to the world than strict geography, and the various people who have to deal with the people and cultures in that region are worried about a lot of things other than some lines on a map, or which piece of land technically sits on which continent or which tectonic plate.