Is the Middle East a part of Africa or Asia?

There is an argument that the Middle East is part of both continents and a part of neither as well. The term transcontinental region might be the best response to this question. The Middle East is a historical and political region of Afro-Eurasia with no clear boundaries. The term "Middle East" was popularized around 1900 in Britain; it has a loose definition traditionally encompassing countries or regions in Western Asia and parts of North Africa. Many have criticized the term Middle East for what they see as Eurocentrism, because it was originally used by Europeans and reflects the geographical position of the region from a European perspective. It is also criticized due to the fact that the term today is often used to only refer to the Arab world, making the situation more confused.
https://en.wikipedia.org/wiki/Middle_East

Geographic explanation:

The Middle East is a geographical and cultural region located primarily in western Asia, but also in parts of northern Africa and southeastern Europe. The western border of the Middle East is defined by the Mediterranean Sea, where Israel, Lebanon, and Syria rest opposite from Greece and Italy in Europe. Egypt in Africa also borders the Mediterranean and is sometimes considered as part of the Middle East, while Turkey and Cyprus literally connect Europe to Asia and oscillate between being called European and Middle Eastern.

http://www.worldatlas.com/webimage/countrys/me.htm

The modern definition of the region includes: Bahrain, Egypt, Iran, Iraq, Israel, Jordan, Kuwait, Lebanon, Oman, the Palestinian territories, Qatar, Saudi Arabia, Syria, Turkey, the United Arab Emirates, and Yemen.

Egypt, with its Sinai Peninsula in Asia, is considered part of the Middle East, although most of the country lies geographically in North Africa. According to international media, North African nations without Asian links, such as Libya, Tunisia and Algeria, are increasingly being called North African.
https://en.wikipedia.org/wiki/Middle_East

According to this site, though, the Middle East is all in Asia, excluding Egypt.
http://www.worldatlas.com/webimage/countrys/me.htm