The biblical reasons for using unleavened bread are present in the gospels according to saints Matthew, Mark, and Luke. In these gospels it is noted that the last supper took place when the feast of unleavened bread was already under way. The words are repeated in each of these gospels. Here are the relevant passages.
Now the first day of the feast of unleavened bread the disciples came to Jesus, saying unto him, Where wilt thou that we prepare for thee to eat the passover? (Matthew 26:17)
And the first day of unleavened bread, when they killed the passover, his disciples said unto him, Where wilt thou that we go and prepare that thou mayest eat the passover? (Mark 14:12)
Then came the day of unleavened bread, when the passover must be killed. (Luke 22:7)
Reading the context one sees that these verses set the scene for the last supper implying that unleavened bread was the bread broken and said to be the body of Christ.