In the daf last week, the Gemara (Menachot 53) addressed the prohibition to make menachot out of chametz. Menachot, grain sacrifices, are usually made as matzah, unleavened bread. There are some, notably the shetei ha'lechem, the two loaves that are brought on Shavuot, which are chametz. Nevertheless, such chametz offerings are never burned on the altar, and the Torah explicitly prohibits this: "For all leaven and all honey you shall not offer up as a burnt offering to God" (Vayikra 3:11).
What is the special problem with chametz on the altar? There are two major approaches to this question.
One approach sees chametz as representing death and decay. This is a theme that plays out in a lot of literature around Pesach, and here it is adopted by, among others, Jacob Milgrom in his commentary:
... Fermentation is equivalent to decay and corruption and for this reason is prohibited on the altar...
"Leaven in the dough" is a common rabbinic metaphor for man's evil propensities (e.g., B. Ber. 17a). The New Testament (sic.) mentions "the leaven of malice and wickedness" (1 Cor 5:8)... This view is shared by the ancients: "Leaven itself comes from corruption and corrupts the dough with which it is mixed ... and in general, fermentation seems to be a kind of putrefaction" (Plutarch, Quaest. Rom. 109)... [These sources] undoubtedly reflect an older and universal regard of leaven as the arch-symbol of fermentation, deterioration, and death and, hence, taboo on the altar of blessing and life.
Jacob Milgrom, Leviticus 1-16, Anchor Bible Series, pp. 188-190
The association with decay and death also connects to the theme of corruption, haughtiness, and evil. Yeast and fermenting of dough causes change, it causes rising (a "puffing up" of self), and it makes simple food into an indulgence. These are all evil things, and must be destroyed on Pesach and kept off the altar at all times.
In contrast to the above approach is that of Rambam. Rambam in the Guide (III:46), understands that this prohibition - like many others related to the Temple - was to keep away pagan practices:
The idolaters did not offer any other bread but leavened, and chose sweet things for their sacrifices, which they seasoned with honey.... Our Law therefore forbade us to offer leaven or honey...
Why exactly leaven is singled out to be prohibited is not spelled out by Rambam. It seems, however, that leaven may have played a specific role in fertility rituals. Because leaven represents fermenting and change, it can also represent fecundity. True there is decay and death, but this is part of the natural cycle, and with this decay and death comes new life. The earth lays "dead" all winter, and then in the spring and summer, the seeds that were planted in the fall, and have decayed and died, now rise out of the ground and bring new life. [This is also why in the brakha of mechayeh ha'meitim the resurrection of the dead is compared to the rain bringing life to the seeds, causing grain to rise out of the ground.]
And, while we are talking about fertility, let us not forget that leaven causes the bread to puff up, like a pregnant woman. These are all powerful images, and it would seem that leaven would have played an important role in pagan fertility rituals.
Thus, the Torah would specifically be prohibiting leaven - of all products used in pagan sacrifices - because it represented the very powerful and alluring fertility rituals of those cults. This explains why the prohibition is coupled in the Torah with the mention of the first fruits:
No meal offering, which you shall bring to the Lord, shall be made with leaven; for you shall burn no leaven, nor any honey, in any offering of the Lord made by fire. As for the sacrifice of the first fruits, you shall offer them to the Lord; but they shall not be burned on the altar for a sweet savor. (Vayikra 2:11-12)
We are dealing with a concern about how to ensure agricultural success in the following year - and what better way to relate to these concerns than through the bringing of a flour sacrifice - a mincha. However, to bring this as a type of fertility symbol, as leaven, is absolutely forbidden. What will you do during the spring, to pray for the success of the crops and to give your thanks to God? You will bring a "sacrifice of first fruits, bikkurim" which - as Rashi points out - refers both to the shetei ha'lechem and the bikkurim themselves. These are brought during Shavuot time exactly for this reason, but they do not get placed on the altar. They are brought into the Temple, but never on the altar itself.
This balance between chametz and matzah is exactly the progression - that we are in the midst of now - from Pesach to Shavuot. At the very beginning of spring, the omer sacrifice of the new grain is brought as matzah, as the fertility of the Earth has yet to express itself, and only the barely has ripened. However, once we are in the middle of the spring, and the fertility is in full flower, the wheat has ripened and the first fruits are emerging, now is the time to bring the sacrifice of the shetei ha'lechem, the chametz sacrifice, and the bikkurim - sacrifices that represents this fertility, and that are both a thanks to God for what God has provided and a prayer for future blessings of the land.
In closing, it should be noted that there is one other prohibition which the Torah links to bikkurim, and which Rambam, and with further clarification, Sforno, relates to concerns about pagan practices. That prohibition is the prohibition of cooking a kid goat in its mother's milk:
The first of the first fruits of your land you shall bring into the house of the Lord your God. You shall not boil a kid in its mother's milk. (Shemot 23:19)
What is this about? Says Rambam:
Meat boiled in milk is undoubtedly gross food, and makes overfull; but I think that most probably it is also prohibited because it is somehow connected with idolatry, forming perhaps part of the service, or being used on some festival of the heathen. I find a support for this view in the circumstance that the Law mentions the prohibition twice after the commandment given concerning the festivals "Three times in the year all thy males shall appear before the Lord God" (Exod. xxiii. 17, and xxxiv. 73), as if to say, "When you come before me on your festivals, do not seethe your food in the manner as the heathen used to do."
Guide for the Perplexed, III:48 (Friedlander ed.).
And the connection not just to the pilgrimage festivals, but to the bikkurim, is explained by Sforno:
"Do not cook a kid goat in its mother's milk" - do not do anything like these activities in order to increase the crops, as the idol worshipers believe, but rather - "the first of the first fruits of your land you shall bring..." as the verse states: "And the first of all of the first fruits, and the donation-offering of all [you shall give to the priests]... to cause a blessing to rest in your house (Ezek. 44:30). (Sforno on Shemot 23:19)
Just as the fermenting power of chametz evokes fecundity, change and growth, the newly born kid goat, and its mother's milk evoke birth, life-giving, and nurturing. The problem, the Torah is saying, is that to cook them together in some fertility ritual, or in a way that echoes such a ritual, both pulls a person into these pagan practices, and - as Ramban emphasizes - replaces ritual for morality. The same ritual whose goal was to increase fertility and fecundity did so at the expense of desensitizing the person to the very life of the animals themselves, through taking these powerful symbols of life, and using them to create food, using the very life-giving milk to turn the kid goat into a dish of meat.
While meat cooked with milk, given this symbolism, is inherently bad, this is not true about chametz. Chametz is how we live our lives the other 11 and 1/2 months of the year. Chametz is fertility, not austerity, and if one learns the lessons of matzah then one can live with chametz and make it part of serving God. We do bring our leaven into the Temple. As the first mishna in our chapter in Menachot states, there are some menachot that must come as chametz. The point is not to overly indulge. To bring these on the altar would be to evoke all the fertility rituals and the inappropriate behaviors that accompanied them. The fecundity of chametz must be given limits, but within those limits, it too becomes a mitzvah.