Is due purely to an accident of geography. Greece is usually contrasted with "Asia Minor", modern day Turkey, as signifying the border between Europe and Asia, but this oversimplifies things. Asia Minor was considered to be part of Asia because Middle Eastern empires like the Akkadian were able to extend their reach there because of lack of natural barriers. Greece, on the other hand, not only had a sea between itself and Asia Minor but was and is extremely mountainous, with the route of invasion over land across the top of the Black Sea being frustrated by mountain ranges and hostile territory, making Greece hard to invade and conquer. Greece therefore developed a culture that was somewhat independent of the cultures of Egypt and the Middle East, although there was an extreme amount of cultural interchange. If you look at linguistics however, the Persians who conquered and influenced Asia Minor spoke an Indo-European language and had some sort of cultural relationship with "Europeans" dating back to prehistory, but they were full participants in Middle Eastern and Central Asian culture and so weren't regarded as part of "Europe". The idea of a unified entity called "Europe" crumbles if you stop looking from Greece west and look at the present day areas that are called Eastern Europe.
Above Greece, in the area north of the Balkan peninsula, there was great interchange between peoples regarded as European today and peoples regarded as non-European, with the result being some terms in Slavic languages today stemming from Persian sources and others. However, since these cultures were different from Middle Eastern ones on the eastern Mediterranean they've been ignored, along with the blurring of the difference between "European" and "Asian" that occurred there. This interchange went north, with the Sarmatian empire, composed of a Persian people, ruling parts of present day Byelorussia as well as most of the Eastern Ukraine, and the Huns later ruling all of Eastern Europe, all of Central Europe, and parts of North West Europe. The Huns were in fact an alliance of Asian, Turkish, Central Asian, and Iranian tribes. Based on some linguistic differences, Baltic and Slavic languages are thought to be closer related to eastern Indo-European languages like Persian than Western European languages. However, the border between East and West itself is porous, with Germanic tribes having cultural interchange with both Slavic tribes and commercial relations with peoples further to the east not normally considered European. Scandinavia and Russia had close relations for quite some time.
In fact, look at the history and prehistory of present day Russia if you want to see how porous the definition of "European" versus "non-European" is. Following Perry Anderson, the author of "From Antiquity to Feudalism", which chronicles the change from the Roman Empire to the feudal states of the middle ages, the only really defining concept of "Europe" as used by people in the United States and England is that the people making it up had cultural contact with the Roman Empire before its fall. But Slavic peoples had contact with the western successor states of the Roman Empire as well as contact with the Byzantine Empire. The Byzantine Empire in turn had its own tradition of cultural expansion, drawing Russia, Bulgaria, and Romania into its sphere and causing a kind of parallel evolution. Yet the Byzantine Empire had Greek and Roman learning as well. Does this make Eastern European states that adopted Orthodox Christianity and Byzantine culture Westerners, in the sense of "True Europeans" (which is what people in the United States generally view Western Europeans as)? What about areas that are on the border, like the Balkans? Are the states of the former Yugoslavia part of the West or the East?
What about Hungarians, who started out as a non-European people, colonized a Slavic area in Europe, but adopted Catholicism and allied themselves to the German Holy Roman Empire?
Eastern or Western?
Hungarian chauvanists will say that they're more cultured than the Romanians due to the influence of being part of the Habsburg empire. The Romanians in turn,heirs of Byzantine culture and of Roman colonization, view the Hungarians as barbaric Asians from the steppes. So are Hungarians east or west?