The issue over whether to use leavened or unleavened bread for the Eucharist is one of the many reasons for the Great Schism of 1054 which split the Church into the Roman Catholic Church and the Eastern Orthodox Church.
If one looks at the actual 11th and 12th century sources, it is the main issue.
The Byzantines saw unleavened bread (άζυμα) as a Judaizing practice, a denial of the new life in Christ, and also as an Apollinarian denial that Christ had a human soul, since the bread had no "soul" in it. See the works of Archbishop Leo of Ochrid, Niketas Stethatos, or even the 13th century records of the union negotiations at Nymphaeum. The main issue was Christological for the Byzantines: only those who deny some aspect of the Incarnation, and Christ's presence in the bread, would use a flat, lifeless, Jewish-inspired, Old Law-style bread for Holy Communion. There were also linguistic and historical arguments, e.g. the Scripture talks of Christ using άρτος (leavened bread), not άζυμα (unleavened).
The Latins/Germans, in turn, said the Byzantines were Judaizers for not shaving their beards, as if they were Nazarenes.
In short, there were a lot of polemics having to do with liturgical customs. Both sides believed they had the original tradition and explained the significance of those traditions with various theological arguments. Very, very few of the polemical works discussed the
filioque: that had more or less reached a detente after the healing of the Photian schism, although it could obviously pop up as another example in the long list of contested practices.
Modern scholars have shown that both leavened and unleavened bread were used in the early centuries, but that leavened became the norm for several centuries, to be replaced in the West no later than the time of Bede. Armenians, however, started to use unleavened a bit earlier. It may actually be the Byzantine dislike for Armenians that played a role in their dislike of the unleavened bread they saw in the Latin rite churches in Constantinople in the 11th century. Also, they didn't like that the new German-backed Pope was making the Byzantine Rite churches in Italy use it.
So, in summary, leavened bread had been the most common thing for some time, but it became common in the West to use unleavened bread for centuries leading up to the 11th century, and, as Cardinal Humbert pointed out, the Byzantines had stopped giving communion in the hand, which was the most ancient of all.
Basically, no one knew about how diverse Christian liturgical practices had been, and assumed their way was the only way ever. As for why this became such a big issue: Much easier to get excited about something tangible like this. Just look at people's visceral (and theological) responses to those who have used or proposed using something like Doritos and Pepsi for communion today; or, less extreme, the polemics one can find over beards and clerical attire.
