Objection 1. It seems that this sacrament ought not to be made of unleavened bread. because in this sacrament we ought to imitate Christ's institution. But Christ appears to have instituted this sacrament in fermented bread, because, as we have read in Exodus 12, the Jews, according to the Law, began to use unleavened bread on the day of the Passover which is celebrated on the fourteenth day of the moon; and Christ instituted this sacrament at the supper which He celebrated "before the festival day of the Pasch" (John 13:1-4). Therefore we ought likewise to celebrate this sacrament with fermented bread.
Objection 2. Further, legal observances ought not to be continued in the time of grace. But the use of unleavened bread was a ceremony of the Law, as is clear from Exodus 12. Therefore we ought not to use unfermented bread in this sacrament of grace.
Objection 3. Further, as stated above (65, 1; 73, 3), the Eucharist is the sacrament of charity just as Baptism is the sacrament of faith. But the fervor of charity is signified by fermented bread, as is declared by the gloss on Matthew 13:33: "The kingdom of heaven is like unto leaven," etc. Therefore this sacrament ought to be made of leavened bread.
Objection 4. Further, leavened or unleavened are mere accidents of bread, which do not vary the species. But in the matter for the sacrament of Baptism no difference is observed regarding the variation of the accidents, as to whether it be salt or fresh, warm or cold water. Therefore neither ought any distinction to be observed, as to whether the bread be unleavened or leavened.
On the contrary, According to the Decretals (Extra, De Celebr. Miss.), a priest is punished "for presuming to celebrate, using fermented bread and a wooden cup."
I answer that, Two things may be considered touching the matter of this sacrament namely, what is necessary, and what is suitable. It is necessary that the bread be wheaten, without which the sacrament is not valid, as stated above (Article 3). It is not, however, necessary for the sacrament that the bread be unleavened or leavened, since it can be celebrated in either.
But it is suitable that every priest observe the rite of his Church in the celebration of the sacrament. Now in this matter there are various customs of the Churches: for, Gregory says: "The Roman Church offers unleavened bread, because our Lord took flesh without union of sexes: but the Greek Churches offer leavened bread, because the Word of the Father was clothed with flesh; as leaven is mixed with the flour." Hence, as a priest sins by celebrating with fermented bread in the Latin Church, so a Greek priest celebrating with unfermented bread in a church of the Greeks would also sin, as perverting the rite of his Church. Nevertheless the custom of celebrating with unleavened bread is more reasonable. First, on account of Christ's institution: for He instituted this sacrament "on the first day of the Azymes" (Matthew 26:17; Mark 14:12; Luke 22:7), on which day there ought to be nothing fermented in the houses of the Jews, as is stated in Exodus 12:15-19. Secondly, because bread is properly the sacrament of Christ's body, which was conceived without corruption, rather than of His Godhead, as will be seen later (76, 1, ad 1). Thirdly, because this is more in keeping with the sincerity of the faithful, which is required in the use of this sacrament, according to 1 Corinthians 5:7: "Christ our Pasch is sacrificed: therefore let us feast... with the unleavened bread of sincerity and truth."
However, this custom of the Greeks is not unreasonable both on account of its signification, to which Gregory refers, and in detestation of the heresy of the Nazarenes, who mixed up legal observances with the Gospel.
Reply to Objection 1. As we read in Exodus 12, the paschal solemnity began on the evening of the fourteenth day of the moon. So, then, after immolating the Paschal Lamb, Christ instituted this sacrament: hence this day is said by John to precede the day of the Pasch, while the other three Evangelists call it "the first day of the Azymes," when fermented bread was not found in the houses of the Jews, as stated above. Fuller mention was made of this in the treatise on our Lord's Passion (46, 9, ad 1).
Reply to Objection 2. Those who celebrate the sacrament with unleavened bread do not intend to follow the ceremonial of the Law, but to conform to Christ's institution; so they are not Judaizing; otherwise those celebrating in fermented bread would be Judaizing, because the Jews offered up fermented bread for the first-fruits.
Reply to Objection 3. Leaven denotes charity on account of one single effect, because it makes the bread more savory and larger; but it also signifies corruption from its very nature.
Reply to Objection 4. Since whatever is fermented partakes of corruption, this sacrament may not be made from corrupt bread, as stated above (3, ad 4); consequently, there is a wider difference between unleavened and leavened bread than between warm and cold baptismal water: because there might be such corruption of fermented bread that it could not be validly used for the sacrament.
Source: Summa Theologica (New Advent)