Why does the Eastern Orthodox Church reject papal infallibility, the Immaculate Conception, and purgatory?
In any discussion with the Orthodox, it is important to begin by finding out what they mean by infallibility or immaculate or purgatory. In my experience, it is rare to find among them someone who has a clear understanding of the meaning of these doctrines as they are expressed in the Latin Church. If they do understand what we mean by these doctrines, then they begin to see them not so much as real doctrinal differences but as different expressions of the same Faith.
The tradition of the Latin Church has teachings—regarding the last things, the nature of original sin, the sacraments, and the role of the bishop of Rome—that are simply the result of the mostly North African Latin (Cyprian through Augustine) theological tradition, which was then popularized by St. Gregory the Great and really creates the medieval Western synthesis.
There are Orthodox who are intent on finding doctrinal errors wherever there are simply differences of expression. The Latin Church has always been more flexible, even if not perfectly so, about differences of rite and tradition between East and West, but it has been very hard for the Orthodox to have the same flexibility for various historical reasons. The fact is that the Roman Church is in active communion with local churches that share the fullness of the Eastern traditions, but the Eastern Orthodox have a very hard time even imagining a legitimate Latin expression of the Orthodox faith.
The very few parishes they have that follow a "Western" (basically high-church Anglican) liturgy have to submit to all kinds of Easternizations. The Roman Church has usually worked to maintain the integrity of the Eastern rites, not always successfully (although this had more to do usually with the interference of civil powers—as in Austria, Hungary, and Poland—than with the Church), but rather consistently. Among the Orthodox it is hard to get a consensus even about the validity of our baptism and Eucharist. So it is not surprising that some of their zealots will not be interested to understand our tradition or to accept its basic compatibility with theirs.
On the ground, though, the Orthodox are usually open and reasonable. It is often just the converts from Protestantism and Catholicism, along with some of the monastics and ultra-nationalists, who are unwilling to accept the authenticity of our Tradition. But we should always recognize theirs and never fall into the same type of zealotry.