Why is even a tiny piece of Chametz forbidden on Pesach? Radvaz (Rabbi David ben Zimra, 1479-1573) askes this question in She'elot uTeshuvot Radvaz, 3:546 (977). After finding that there is no other halacha that makes quite such stringent demands, he concludes that this is because chametz symbolizes the yetzer hara (evil inclination). One place where this idea is expressed is in Brochos 17a, where it says that when Rabbi Alexandari finished saying the amidah, he would add a tefillah: "Master of the Universe, You know full well that it is our desire to act according to Your will; but what prevents us from doing so? The se’or in the dough..." This also the reason why we expend such a tremendous effort seeking out and clearing away chametz before Pesach. I can say that this thought helped me tremendously, for it makes what is otherwise a dreary and difficult task into an inspiration. The message is that there is zero tolerance for the yetzer hara.
However, there is a problem. In his sefer about the reasons for mitzvos, Radvaz raises the following objection: If chametz represents the yetzer hara, why then is it allowed the rest of the year? He presents two answers:
The first answer is that matzah is hard on the stomach! According to the Radvaz, it would indeed be preferable spiritually to eat matzah and ban chametz all year round, but that is not practical. For this reason, Torah limits the war on chametz to one week a year. He likens it to Yehoshua’s circling of the walls of Yericho for seven days.
The second answer of the Radvaz is that the reason that Hashem gave us the yetzer hara is to test us to see if we can withstand it. After all, the world needs the yetzer hara. If not for its life force, everything would come to a grinding halt. The Gemara recounts that the rabbis once prayed that the yetzer hara for women be removed. Hashem granted their request -- but hens would not produce eggs(Yoma 69b). This is why chametz is permitted all year-round -- as a test to see if we can overcome our yetzer hara.
This also relates to the concept that all chumros are permitted on Pesach. A common Chabad teaching is that "Pesach is Andersht", that is, that all kinds of chumros, with or without a clear source, are laudable on Pesach. The Mei HaShiloach quotes Reb Bunim MiParshischa who said that all the stringencies that the Jewish People adopt on Pesach are adornments to holiness, and this is alluded to in the verse that states (Shir HaShirim 1:!0) tzavareich bacharuzim, your neck with necklaces. This means that every limb of a person’s body has a corresponding ornament or garment, whereas the neck can be adorned with an ornament that is not unique to the neck. A precious stone is not designed to clothe someone. Rather, it is intended to be suspended from a person’s neck. Similarly, the stringencies that have been adopted by the Jewish People on Pesach is due to the fact that the neck is the vehicle through which the food enters, and it is specifically regarding food matters that all the stringencies on Pesach apply.
Here is how I understand this concept. Generally, a chumra is praiseworthy thing and an expression of loving G-d, except that a person should not take on stringencies that are far above his or her current level of observance. Doing so exposes his other deficiencies and represents Kefitsas Hamadreigos which is not the right way in serving Hashem. However on Pesach even chumros that are far above the observance level are fully legitimate. Pesach is the time of mortal combat with Yetser Hara and in a fight to the last, any weapon is acceptable. It is no dishonor to a warrior in the midst of the battle to slay his enemy with a tree trunk, should a sword not be available. Similalry, Pesach is a "time-out" during which the usual cosiderations in Derech Hoavoda do not apply.
Mesilar Yesharim writes in Ch. 18:
We notice at all periods and at all times, between all lovers and friends - between a man and his wife, between a father and his son, in fine, between all those who are bound with a love which is truly strong -that the lover will not say, "I have not been commanded further. What I have been told to do explicitly is enough for me." He will rather attempt, by analyzing the commands, to arrive at the intention of the commander and to do what he judges will give him pleasure. The same holds true for one who strongly loves his Creator; for he, too, is one of the class of lovers. The mitzvoth, whose behests are clear and widely known, will serve as an indication to him of the will and desire of the Blessed One. He will not say, "What has been explicitly stated is enough for me," or "In any event I will discharge my obligations by doing what is incumbent upon me." To the contrary, he will say, "Since I have seen that God's desire inclines towards this, I will use it as a sign to do as much as I can in relation to it and to extend it into as many areas as I can envisage the Blessed One's desiring its being extended into." Such a man may be called "one who gives pleasure to his Creator."
For a different perspective, at least in the public sphere, see here and here (From Sichos Haran). Also an argument that even on Pesach chumros must be examined for reasonableness and source.
