My answer, which only represents me and no church group, is halfway between 'this is the true faith and everything else is bogus' and 'no reason - it's all personal'.
'This is the true faith etc.' seems an unassailable reason, though. But to deny that 99.9999% percent of the time
Western Catholicism and
Eastern Orthodoxy believe the same things seems like wilful blindness. (Popular with people from xenophobic Eastern European cultures and with those from Protestant backgrounds who can retain their no-popery.)
Other than that, some good reasons might be...
... like the late Fr Lev (Gillet), 'A Monk of the Eastern Church' (I know, he might have been Catholic all along, but anyway), seeing the same light, only clearer. Just as good as Tridentine Roman Catholicism but with a mystical kick to it all its own, which may partly explain why it's still here.
Firstly, unlike Roman Catholicism, Orthodoxy does not believe in or teach the development of doctrine. The Orthodox faith of today is the same as the Orthodox faith in 1700 or 1300 or 900, it doesn't change every few hundred years. It seems that the Orthodox Church holds the true faith without adding to it, as Roman Catholicism has done, and without subtracting from it, as Protestantism has done.
High Church Anglicans have claimed the same thing, and they and the Orthodox who use this argument have a point, though, as Saint Polycarp points out, it isn't airtight. What grabbed me when I first read
The Way of a Pilgrim 12 years ago wasn't the Jesus Prayer (and that never has grabbed me) but that here was
the basic Catholic faith I'd believed in all along, disfigured around me by Vatican II and its aftermath but here, in what happened to be 19th-century Russian form, in a full, glorious form - reinforcing an impression I already had from reading and,
far more important, actually popping into
Byzantine Catholic and Russian Orthodox services starting in 1985. (No 'Wobegonograd' illusion.)
So if one goes to one of their churches and has a combination 'Russians gobsmacked in Hagia Sophia' and
d+¬j+á vu ('but that's what I always believed') experience, that seems to be a pretty good reason. (Liking the people and culture of the ethnicity of that local church doesn't hurt either. I happen to like learning foreign languages.)
Eastern Orthodox are a tiny minority in Western countries but at their churches and institutions you can be assured you won't find the apostolic ministry compromised - ever, won't have reason to doubt that what is being offered you is
the Body and Blood of Christ in the Sacrament or find teachers claiming that Jesus wasn't really God, had brothers and sisters, had sex, etc. (So-called, common-knowledge 'Catholic' institutions do that now. They represent a kind of mainline Protestantism for non-Anglo-Saxons.)
Lest this degenerate into 'East, good; West, bad' crowing, I will admit that too many Eastern Orthodox have sold out on contraception (funny how 'doctrinal development' to ditch the Fathers becomes OK when it has to do with what one does with the genitals) and that there is massive, deafening indifference to
abortion, even though all the Orthodox churches condemn it.
Also, that the
historic mainstream of Western Catholicism also contains this basic
Catholic truth and that its liturgy, the Roman Mass (in pre-1969 form), is just as venerable (and that is without the byzantinizing 'corrections' the will-o'-the-wisp 'Western Orthodox' dare make to it) as the Byzantine and other Eastern rites. (The fact that the consecration prayer hasn't got an explicit
epiklesis points to the fact that it's
older than most of the Eastern rites, except perhaps the Assyrian Rite.)
Pace carpo-rusyn's Pollyannish apologi+ª for the current 'Vatican II' RC regime, I can stand with that mainstream, East
and West, and say, essentially, 'never mind the bollocks'.
Institutional Eastern Orthodoxy in Western countries is a precarious thing, often degenerating into caricature - a small, b*tched-up ethnic chaplaincy pretending to be a universal church.
But what matters is what's contained in Eastern Orthodoxy
is universal.
