In general, when a forbidden food becomes mixed with a permitted food, it is batel be-shishim (rendered insignificant if the forbidden food constitutes less than one sixtieth of the mixture); in such small quantities, it does not contribute flavor. At the level of Torah law, ḥametz is also batel be-shishim. The Sages, however, ordained that even a drop of ḥametz render a permitted food forbidden when mixed with it. Even if the quantity of permitted food is a thousand or ten thousand times greater than the ḥametz, the entire mixture becomes forbidden.
The Sages added this stringency because the Torah itself is more stringent about ḥametz than other forbidden foods: 1) Generally, if one consumes a Torah-forbidden food, the punishment is malkot (lashes), but one who eats ḥametz incurs the more severe punishment of karet (extirpation). 2) Whereas all other forbidden foods may be kept in one’s home, ḥametz can neither be seen nor be found in our homes throughout Pesaḥ. The Sages therefore continued in this direction by establishing a safeguard: even if a drop of ḥametz falls into a food, it is forbidden to consume or derive benefit from it. 3) All other forbidden foods are prohibited throughout the year, and we are therefore accustomed to distancing ourselves from them, but since we eat ḥametz all year long, we are liable to forget that it is forbidden on Pesaḥ. The Sages, therefore, are more stringent about ḥametz, so that everybody remembers to be careful about it.
This law, that even a drop of ḥametz renders a mixture forbidden, goes into effect with the onset of Pesaḥ. Before Pesaḥ, ḥametz is batel be-shishim like all other forbidden foods. Although the prohibition against eating ḥametz and the mitzva to dispose of ḥametz go into effect at midday on the 14th of Nisan, the law that ḥametz is not batel be-shishim does not take effect until Pesaḥ begins, when one who consumes ḥametz incurs karet and when the prohibition of bal yera’eh and bal yimatzei take effect (SA 447:2).
The reasons for strictness about ḥametz are mentioned by Rashi, Rosh, Smak, Rabbeinu Yona, and many others. The first reasons are the principal ones, and therefore ḥametz becomes forbidden in a tiny quantity only once Pesaḥ begins. However, Rambam and Ramban explain that the reason a tiny amount of ḥametz is forbidden is that after Pesaḥ it will again become permitted, since on the Torah level ḥametz she-avar alav ha-Pesaḥ is permissible, and anything that will become permissible in the future (davar she-yesh lo matirin) is not batel in any mixture. According to this opinion, the tiniest amount of ḥametz is forbidden from midday of the 14th. (This is the case only if it is mixed with the same sort of food item [min be-mino]. But the tiniest quantity of ḥametz renders a mixture with dissimilar items [min be-she’eino mino] forbidden only with the onset of the holiday, as explained in Magid Mishneh and Kesef Mishneh [MT, Laws of Ḥametz and Matza 1:5]. And according to Ran, there is a basis to forbid a mixture already from midday of the 14th, based on the rationale that we are not used to avoiding ḥametz. Accordingly, there are grounds to forbid a mixture with even the tiniest amounts of ḥametz starting from midday of the 14th, even min be-she’eino mino.) Nevertheless, SA 447:2 rules that tiny amounts of ḥametz render a mixture forbidden only once Pesaḥ begins, and most Aḥaronim accept this view.