I think "Byzantine" Art is related to Western Art but it isn't just a "part" of it. I think it has a distinct [how should I put this?]... "philosophical" foundation than Western Art. For me the "Western" world is defined mainly in comparison with Byzantium, so there is a difference, even if we are in the same "family".
My impression is that word "Western Art" has been constructed in contrast to all other Arts - Chinese, Arabic, Pre-Columbian, ... not primarily in contrast to Byzantine Art. Term "Western Art" is pretty vaguely defined. It is definitelly not based on geographic principle. But it is also not based on the principle of faith, since then Byzantium would be included. For me, Western Art is Christian Art. Christianity emerged in Middle East, not in England or France, and indeed, Middle East was the West for the Three Kings who came from the far East to pay respect to newly born Christ. So all Christian art should be called "western" if we don't want to discard term "western" alltogether.
Different "philosophical" foundation of "Byzantine" and "Western Art"? - I think, "philosophical" foundation was the same in the first 1,000 years, when there was unity between Rome and other Patriarchal sees. It is more Christian foundation then "philosophical". But after 1054, slowly but surely, and especially after St. Thomas Aquinas, and his "system", various philosophies emerged in the West, and took over theology, and later defined these differences between the "West" and "Byzantium".
see also:
http://hydrogen.pallasweb.com/cgi-bin/yabb/YaBB.cgi?board=history;action=display;num=1121353312;start=0
This link is not working.
There is another major problem. The lack of cooperation between "Post-Byzantine" Orthodox Countries. Romantic nationalism has divided orthodox nations into enclaves with little cultural exchange between them, much in contrast with "Byzantium". Even if "Byzantine" Orthodox ethos includes national/local cultural traditions with much more flexibility than "Western" Christianity, this advantage has become a disadvantage by ignoring each other. This is a product of a complicated history, but there is no reason for it to continue today.
So there is little surprise that the discourse about "Byzantium" is dominated by "Western" views and terms.
I agree with this. But maybe Turkish conquest played some role too. When "Byzantine studies" were 'in statu nascendi' in western Europe, most of the Orthodox countries were still occupied by Otoman Empire. So, later, we all learned about Byzantium and its culture and Art from already established sources in the West, which in the meantime became dominant power, and thus able to dictate both terminology, approach, and the yard-stick with which everybody had to measure "other" arts and cultures.
But the truth is - as you said, that by ignoring each other, and taking national differences as more important than cultural similarities inherited from the Eastern Roman empire, Orthodox countries lost their "Byzantine Commonwealth" and the opportunity to participate and, indeed to lead, in defining what "Byzantine" actually is.
How true and sad is what you sad: "Romantic nationalism has divided orthodox nations into enclaves with little cultural exchange between them, much in contrast with "Byzantium" ", especially when you think that romantic nationalism was invented in western Europe, and then imported in Orthodox countries. (One can think of other parallels: Marxism was also invented in western Europe, not in Russia, or Bulgaria, and then imported in Orthodox countries).
I hope too that there is no reason for this fragmented life of post-Byzanitine countries to continue to exist today. As far as I follow, I am pleased to see increased cooperation, for instance, in Astronomy research between Bulgaria and Serbia. I believe there are other encouraging examples of cooperation.
Regards,
Branislav