One thing worth considering is that, since relative land area isn't a number most people have to hand, and it's not a very intuitive way of thinking about geography, relative land area just isn't an important factor in deciding which continent we think a country is part of.

Turkey has at least two major cities in Europe, and its European region consists of four provinces. The center of Turkey's largest city is in Europe. Historically, the Ottoman Empire had major territorial possessions in Europe. It is difficult to really talk about Turkey in geographic or historical terms without giving credence to the fact that it is considered part of both Europe and Asia, because the European part is so prominent and not just a backwater afterthought.

Egypt has... Sinai?

It's also worth noting that the border between Europe and Asia is probably more culturally important, and definitely more important in Western history and literature, than the border between Asia and Africa. Egypt's status as intercontinental nation isn't really an important aspect of its perception on the world stage or its cultural identity, as is the case of Turkey.

Also keep in mind that our concept of continents is shaky, at best, and really a cultural artifact rather than a scientific black and white reality. I mean, it's also kind of nuts that we consider Greenland part of North America, but Iceland is part of Europe. And what is even up with Oceania?