Would you consider Pakistan to be a South Asian or a Middle Eastern country?
The question is very much like "would you consider phknrocket1k a partisan hack or a troll?" in the sense that they aren't mutually orthogonal groups. For example, Israel and Jordan are clearly in Asia, but obviously they're at the heart of the middle east. ("Ash-sharq al-awsat" I think the arabs call it, literally, "The Middle East") Better example: the Sinai peninsula is politically part of an African country, geographically part of Asia, and is in fact at the heart of the middle east.
Sorry, maybe that's unfair, and a little misleading, since the region we call The Middle East is entirely different from the region we call "South Asia" (The latter being the Indian Subcontinent: India, and two countries which, until the mid-20th century, were part of India, Pakistan and Bangladesh; and perhaps you could lump some neighboring lands such as nepal, afghanistan, and burma into "south asia" at a stretch, a long one.) I don't think any demographers, political scientists, or geographers consider any of the "stans" (persian for "lands") as part of the middle east. (Afghanistan, Pakistan, Turkmenistan, Kyrgistan, Uzbekistan, etc. are the Stans.) Kurdistan, if and when it comes into independent existence, may well be the first Stan to be part of the middle east, though. But that would be a bit of an embarassment for the Bush administration, so it may not be allowed to happen.
I agree with Lewis' comment about Iran, since the arabic peoples don't historically call it part of ash-sharq al-awsat, but it doesn't fit neatly into Central Asia or the Indian Subcontinent either. Here's an idea: let's just call it Iran and be done with it.