I think the reason Catholics used unleavened bread is because it was used at the Last Supper.
There is great debate about which bread was used at the Last Supper. Scholars believe that the question will never be answered.
But there is no doubt that the Church of Rome used leavened bread, and not unleavened bread, for the first 1000 years while she was in communion with the Churches of the East. The change to the present use of unleavened bread was taking place at the same time as the Great Schism between us.
Fr. Joseph Jungman – in his book The Mass of the Roman Rite – states that,
"In the West, various ordinances appeared from the ninth century on, all demanding the exclusive use of unleavened bread for the Eucharist. A growing solicitude for the Blessed Sacrament and a desire to employ only the best and whitest bread, along with various scriptural considerations – all favored this development.
“Still, the new custom did not come into exclusive vogue until the middle of the eleventh century. Particularly in Rome it was not universally accepted till after the general infiltration of various usages from the North” [Rome adopted unleavened bread only a few years after the schism with the East.]
– Joseph Jungman, The Mass of the Roman Rite, volume II, pages 33-34
And Fr. Jungman goes on to say that,
“. . . the opinion put forward by J. Mabillon,
Dissertatio de pane eucharistia, in his answer to the Jesuit J. Sirmond,
Disquisitio de azymo, namely, that in the West it was always the practice to use only unleavened bread,
is no longer tenable”
– Jungman, The Mass of the Roman Rite, volume II, page 33.
Now, the fact that the West changed its practice and began using unleavened bread in the 8th and 9th century – instead of the traditional leavened bread – is confirmed by the research of Fr. William O’Shea, who noted that along with various other innovative practices from Northern Europe, the use of unleavened bread began to infiltrate into the Roman liturgy at the end of the first millennium, because as he put it,
“Another change introduced into the Roman Rite in France and Germany at the time * was the use of unleavened bread and of thin white wafers or hosts instead of the loaves of leavened bread used hitherto”
– Fr. William O’Shea, The Worship of the Church, page 128.
Moreover, this change in Western liturgical practice was also noted by Dr. Johannes H. Emminghaus in his book, The Eucharist: Essence, Form, Celebration, because as he said:
“The Eucharistic bread has been unleavened in the Latin rite since the 8th century – that is, it is prepared simply from flour and water, without the addition of leaven or yeast. . . . in the first millennium of the Church’s history, both in East and West, the bread normally used for the Eucharist was ordinary ‘daily bread,’ that is, leavened bread, and the Eastern Church uses it still today; for the most part, they strictly forbid the use of unleavened bread. The Latin Church, by contrast, has not considered this question very important.”
– Dr. Johannes H. Emminghaus, The Eucharist: Essence, Form, Celebration, page 162]
Thus, with the foregoing information in mind, it is clear that the use of leavened bread by the Eastern Churches represents the ancient practice of the undivided Church, while the use of unleavened bread by the Western Church was an innovation introduced near the end of the first millennium.*