The Torah mentions several times that the purpose of all the miracles connected with Yetziat Mitzrayim was to demonstrate the existence of God, his power, and all the principles of our faith to the Jewish people. Pesach was designated as the Yom Tov of Emunah and the matzah is called, "the food of emunah", by the Zohar. Shavuot is the Yom Tov of receiving the Torah.
The "Kedushat Levi" points out the contrast between the two Yomim Tovim: 1. On Pesach we may not even possess any chametz, as opposed to Shavuot which is the one and only time in the year that a korban is brought from chametz, The Talmud considers the "shtei halechem" brought on Shavuot as a more elegant korban because of the fact that it consists of chametz. 2. The "minchat haomer" brought on Pesach is most unusual as it consists of barley grain, as opposed to almost all other minachot, including the "shtei halechem", which all come from wheat. Barley is usually used to feed the animals, as opposed to wheat, which is traditionally used for human consumption.
It may well be that these contrasts are due to the differences between the themes of the two Yomim Tovim. Pesach represents emunah, and regarding our understanding of God we must all have the attitude that, "if I really understood Him, I would be Him" (Kuzari). None of us can really understand any aspect of Elokut. Our understanding is compared to that of the animals (see Tehillim 73:22, and 42:2; Tanya Chapter 18). The "omer" korban on Pesach must consist of maachal beheima to emphasize this idea. No chametz is permitted at all since matzah represents elementary simplicity, while chametz represents sophistication. On Shavuot when we celebrate Torah learning the "shtei halechem" korban should be maachal adam representing the idea that we were commanded to use our human intelligence to the best of our ability to delve into the study of the Torah. That korban must be made into chametz, representing the sophistication one should attain in Torah learning.
But, sophistication is not necessarily a trait that we want to develop in regards to emunah. The Chasid Yavetz (who was among the Jews who were expelled from Spain in 1492) wrote that he noticed the percentage of Jews who converted to Christianity to save their lives was much higher among those who were philosophers than among the peshutei haam who adhered to an emunah peshutah.
If one delves deeply into Torah learning his faith will neither remain simplistic nor primitive. Our tradition teaches us that the Torah is a description of Elokut. (This is the meaning of the concept of "mashal hakadmoni" See Rashi on Shemot 21:13.) Moshe Rabbeinu was the only prophet to whom the Torah was revealed, and this is referred to by the Torah as his, "having had a glimpse of the image of God." (Bamidbar 12:8). The best way to develop a love of God is by learning His Torah. (See Rashi on Devarim 6:6). By gaining Torah knowledge and developing a sophisticated approach to Torah, which is a description of Elokut, we come to understand Him better and our emunah becomes enhanced.