Transsubstantiation is taught by the Catholic Church and is treated as compatible with the Orthodox teaching, and as far as I know with all other Churches (pre-Chalcedon) that have a valid apostolic succession. This is therefore a part of the teaching as commanded by Christ in his Great Commission to the apostles, which is a scriptural fact. The other teachings do not have similar historical or scriptural continuity.
Note that the appeal here is not to antiquity as such, although we certainly have that in this case, but to validity of the teaching commission.
I could VERY well be wrong about this, but I have a vague memory from the L&E thread that the Orthodox don't agree with "something" about Transubstantiation, but I can't remember what it is.
A comparison may be made with orthodox, rabbinic Judaism. Obviously, Judaism rejects Jesus of Nazareth as being the Messiah foretold in the Old Testament as far back as Genesis 3:15, and by Isaiah, Jeremiah, and other prophets. After the fall of the Temple in Jerusalem and the ending of the Jewish commonwealth, the authoritative oral tradition of the rabbis dating back for centuries began to be reduced to writing, forming the basis for the Talmud, which was developed in Jerusalem and Babylon in the 4th and 5th Centuries AD. In turn, the Talmud and the Old Testament (Torah) were authoritatively interpreted by medieval Jewish scholars such as Solomon ben Isaac and Gershom of Mainz.
Orthodox rabbinical Judaism thus has a group of authoritative writings structured similarly to Catholicism and Eastern Orthodoxy (although, like Eastern Orthodoxy and unlike Catholicism, there is no one individual considered to be the visible head of God's people on earth given the authority to "bind and loose."). In terms of time frames and antiquity, the Jewish tradition predates that of the Christian religion by centuries. As with Catholicism and Eastern Orthodoxy, traditional Jews state that there is consistency between the Torah, Talmud, and the commentaries. Excluded from this camp are Karaites (Jewish believers who are "Sola Torah") and Reform and Conservative Jews (essentially theological liberals with a Jewish veneer). If your standard of objective fact are antiquity, consensus, and consistency, then orthodox, rabbinical Judaism would relegate Catholicism and Eastern Orthodoxy to the status of superstition.
Why orthodox Christians reject the authority of the Talmud and the rabbinical commentaries is based on their acceptance of Jesus Christ as the Messiah predicted in the Torah/Old Testament. Given that Jesus Christ Himself condemned the oral traditions of the Pharisees, the Jewish faction that was the progenitor of rabbinic Judaism, the Talmud and the subsequent rabbinic commentators are regarded by all orthodox Christians as invalid with respect to the Christian faith. In other words, the starting points for all orthodox Christian belief are the acceptance of the Old Testament as being the revealed Word of God and the view that Jesus Christ is the anticipated Messiah predicted in the Old Testament.
It is incorrect to say that sola Scriptura is superstition, even though the predominant belief of the pre-Reformation church was that of Scripture and tradition as authoritatively interpreted by the church through its councils and theologians. By the same standard applied to this Protestant doctrine, orthodox, rabbinical Judaism would have grounds to claim that the entire Christian religion is superstition. Ultimately, Eastern Orthodoxy, Catholicism, Protestantism, Judaism, and other religions are constructed on metaphysical presuppositions that are accepted on the basis of faith.