Most commentators take a mild stand on this prohibition for the grain offering. The reason: the text does not really say why. But I think that there is precedence based on symbol. The first has to do with history, the second with a generality.
Starting with Israel’s history, we know that the generation that first received the revelation of the levitical system was the same generation of the Exodus from Egypt. The whole vivid reminder of the sacrificed lamb with blood on the doorposts… eating unleavened bread in haste…all of that was fresh in their minds. So offering a grain offering without leaven was consistent with thanking God for His deliverance.
Generally, leaven is also symbolic of the corruptive influence of sin. Jesus used the metaphor this way (Matthew 16:6-12), as did Paul (1 Corinthians 5:6-8, Galatians 5:9). It would make sense that God would set up these sacrifices in this way and that the people would see this prohibition as instructive.
So in the picture of the grain offering is a prohibition that reminds us that even the smallest of sins are destructive to our relationship with God. We should take holy living and obedience to God seriously.