The laws of the red heifer are unclear and contradictory: While its ashes purify the impure, those involved in the purification of the impure become impure themselves. The Sages referenced the red heifer as the most distinctive paradigm of a mitzva whose rationale is unclear.

King Solomon said: All of these I have solved, but the section of the red heifer I investigated, and asked, and searched; “I said: I will become wise, but it is distant from me” (Ecclesiastes 7:23). The verse states that God told Moses: “[This is the statute of the Torah]…And they shall take to you an unflawed red heifer” (Numbers 19:2). Rabbi Yosei bar Hanina said: The Holy One, Blessed be He, said to Moses: I will reveal the rationale for the heifer to you, but for others, it is a statute. There was an incident involving a certain non-Jew who asked Rabban Yohanan ben Zakkai: You perform several actions that appear like witchcraft: You bring a heifer, burn it, crush it, and take its ashes. If one of you becomes impure with impurity imparted by a corpse, one sprinkles two or three drops upon him and you say to him: You are purified. Rabban Yohanan ben Zakkai said to him: Has an evil spirit ever entered you? The man said to him: No. Rabban Yohanan ben Zakkai said to him: Have you ever seen a person into whom an evil spirit entered? The man said to him: Yes. Rabban Yohanan ben Zakkai said to him: What do you do to him? The man said to him: We bring medicinal roots, burn them beneath the afflicted person, and we sprinkle water on him; then the spirit flees. Rabban Yohanan ben Zakkai said to him: Let your ears hear what your mouth is saying. Likewise, this spirit is the spirit of impurity, as it is written: “I will remove…the spirit of impurity from the land” (Zechariah 13:2); one sprinkles the waters of sprinkling upon it, and it flees. After the non-Jew exited, his students said to him: Our teacher, you dismissed that one with a reed [i.e., with a perfunctory answer]. What do you say to us? Rabban Yohanan ben Zakkai said to them: By your lives, it is not the corpse that renders impure and it is not the water that purifies. Rather, the Holy One, Blessed be He, said: I enacted a statute, I issued a decree. You may not violate My decree, as it is written: “This is the statute of the Torah” (Numbers 19:2). (Bemidbar Rabba 19; Tanĥuma, Hukat)