An Exalted Light
Those involved with the red heifer from beginning to end cause their garments to become impure. Yet it itself purifies garments (Bamidbar Rabbah). The service of the red heifer evokes a revelation from the lofty light of the sefira of Keter. This revelation has a positive effect on the impure person—it purifies him. But the pure person, who does not need such a revelation, falls from his level and becomes impure. It’s like a medicine that heals the sick but harms the healthy. (Ohr HaTorah, the Tzemach Tzedek)
Elixir of Life—or the Opposite
Even in Torah itself we find something similar to the red heifer's paradox: "It purifies the impure and defiles the pure." If one is meritorious, Torah becomes an elixir of life; if not, it becomes a potion of death. (Rabbi David of Lelov)
Defies Logic
There are many other Torah commands whose reasoning is not revealed, like the prohibition of wearing shaatnez (mixed wool and linen). But still, the term “statute” is used only for the red heifer, because this mitzvah not only lacks explanation—it contradicts logic: It purifies the impure and defiles the pure. (Yavin Shemuah)
Education Depends on the Mother
In regards the mitzvah of the red heifer Rashi quotes the Sages: “It’s like the son of a maid who dirtied the king’s palace. They said: Let his mother come and clean up after him.” So too, let the red heifer atone for the sin of the golden calf. This teaches that a child’s education depends primarily on the mother. As the homemaker, she shapes the home’s atmosphere and forms the child’s character. That’s why it says “let his mother come”—and not “let his father come.” (the Rebbe)
In the Same Pot
A few months after the release of the Rebbe Rayatz (Rabbi Yosef Yitzchak Schneersohn) of Lubavitch from imprisonment in Communist Russia, he needed to leave the country and moved to Latvia. When the first anniversary of his release arrived—on the 12th of Tammuz, 5688 (1928)—he was staying at a health resort near Riga, and the chassidim gathered to celebrate the Festival of Redemption with the Rebbe.
During the farbrengen (chassidic gathering), the chassidim began to sing the melody, “Padah B’shalom Nafshi” (“He has redeemed my soul in peace”). The Rebbe instructed them to stop singing and said: “As long as the Jews of Russia are not well—it is not yet a complete redemption. I am with them in the same pot.”