Why do we have Three Matzot and Four Cups of Wine?
Our sages established that we drink four cups of wine at the Seder, recalling the four expressions of redemption that G-d commanded Moses to convey to the Jewish people. These expressions are found in the beginning of parshat Vaera, "I will take you out... I will save you... I will redeem you... And I will take you [to Myself as a nation]..."
If these four expressions of redemption are so significant that they should be symbolized at the Seder, why not have four matzahs? After all, the matzahs are a biblical commandment, which the Mishnah tells us is "because our parents were redeemed from Egypt." So why four cups of wine, which are only a rabbinical enactment?
Why do we need three matzahs? The simple reason is that two whole matzahs are for the hamotzi blessing, just like on every Shabbat or holiday, we make the blessing over two whole loaves. The third, broken piece of matzah (poor man's bread) is to recite the Haggadah over.
However, since everything in Torah is perfect, and we know that the reason we have matzah is "because our parents were redeemed from Egypt," the three matzahs must represent redemption as well.
With this understanding, we can conclude that there are two aspects of redemption: One is connected to the number three, represented by matzah, and the other is connected to the number four and is represented by wine.
What are these two aspects of redemption? And why are they represented by wine and matzah?
We are told that the Israelites had sunken to such a spiritual low in Egypt, that if they would have stayed even a moment longer, they would have been totally lost, with no chance of redemption. It was only that G-d pulled them out in the nick of time. In other words, it wasn't due to their merits or efforts that they were redeemed. Rather it was a unilateral redemption, with G-d doing it Himself.
This is what the Exodus was all about: being redeemed by G-d himself, without our effort. Since it was from G-d and we had no involvement, we have no pleasure in it. This is represented by matzah, which doesn't have much flavor. It is poor man's bread, symbolizing that we were poor in understanding and spirituality. We have three matzot, representing the first three expressions of redemption, "I will take you out... I will save you... And I will redeem you..." These are all one-sided, from G-d himself without our involvement. Since these three actually happened at the Exodus, they are represented by matzah, a biblical commandment.
The fourth, "And I will take you to Myself as a nation," didn't reach completion until we received the Torah at Mount Sinai, after 50 days of working on ourselves. Since it came about through our effort and our merit, we have pleasure in it. It is therefore represented by wine, which has flavor. Since it only reached completion 50 days after the Exodus, it is not totally connected to Pesach, and therefore only a rabbinical enactment.
So you have three that are a given, and the fourth that is developed by the recipient.
Judaic Studies Teacher